Beamforming for wireless power transfer

ABSTRACT

Systems and techniques are provided for beamforming for wireless power transfer. A phase/amplitude map for a notional field in a plane of an aperture of the second wireless power transfer device may be determined. A Fourier transform may be performed on the phase/amplitude map for the notional field to generate a spatial frequency representation of the notional field. A phase/amplitude map for a second notional field in a plane of an aperture of the first wireless power transfer device may be determined based on the spatial frequency representation of the notional field and the position of the second wireless power transfer device. Control signals for transducer elements of the first wireless power transfer device may be generated based on the determined phase/amplitude map for the second notional field. The control signals for the transducer elements may be supplied to the transducer elements.

BACKGROUND

Ultrasonic waves may be used to transfer power wirelessly betweenultrasonic transducers. Multiple ultrasonic transducers may be used totransmit power to multiple ultrasonic transducers. The amount of usablepower generated by the receiving ultrasonic transducers, and amount ofrectification needed, may be affected by the spatial variations in phaseamong the ultrasonic waves as they are received at the receivingtransducers. The spatial variations in phase may be due to theorientation of the receiving ultrasonic transducers relative to thetransmitting ultrasonic transducers, variations in phase among theultrasonic waves output by the transmitting ultrasonic transducers, andinterference between the ultrasonic waves output by the transmittingultrasonic transducers.

BRIEF SUMMARY

According to implementations of the disclosed subject matter, a positionof a second wireless power transfer device relative to a first wirelesspower transfer device may be determined. A phase/amplitude map for anotional field in a plane of an aperture of the second wireless powertransfer device may be determined. A Fourier transform may be performedon the phase/amplitude map for the notional field to generate a spatialfrequency representation of the notional field in the plane of theaperture of the second wireless power transfer device. A phase/amplitudemap for a second notional field in a plane of an aperture of the firstwireless power transfer device may be determined based on the spatialfrequency representation of the notional field in the plane of theaperture of the second wireless power transfer device and the positionof the second wireless power transfer device. Control signals fortransducer elements of the first wireless power transfer device may begenerated based on the determined phase/amplitude map for the secondnotional field in the plane of the aperture of the first wireless powertransfer device. The control signals for the transducer elements may besupplied to the transducer elements. Waveforms may be transmitted fromthe transducer elements based on the supplied control signals.

Systems and techniques disclosed herein may allow for beamforming forwireless power transfer. Additional features, advantages, andembodiments of the disclosed subject matter may be set forth or apparentfrom consideration of the following detailed description, drawings, andclaims. Moreover, it is to be understood that both the foregoing summaryand the following detailed description are examples and are intended toprovide further explanation without limiting the scope of the claims.

BRIEF DESCRIPTION OF THE DRAWINGS

The accompanying drawings, which are included to provide a furtherunderstanding of the disclosed subject matter, are incorporated in andconstitute a part of this specification. The drawings also illustrateembodiments of the disclosed subject matter and together with thedetailed description serve to explain the principles of embodiments ofthe disclosed subject matter. No attempt is made to show structuraldetails in more detail than may be necessary for a fundamentalunderstanding of the disclosed subject matter and various ways in whichit may be practiced.

FIG. 1 shows an example arrangement suitable for beamforming forwireless power transfer according to an implementation of the disclosedsubject matter.

FIG. 2 shows an example system suitable for beamforming for wirelesspower transfer according to an implementation of the disclosed subjectmatter.

FIGS. 3A and 3B show example arrangements suitable for beamforming forwireless power transfer according to an implementation of the disclosedsubject matter.

FIGS. 4A and 4B show example arrangements suitable for beamforming forwireless power transfer according to an implementation of the disclosedsubject matter.

FIG. 5 shows example waveforms suitable for beamforming for wirelesspower transfer according to an implementation of the disclosed subjectmatter.

FIG. 6 shows example waveforms suitable for beamforming for wirelesspower transfer according to an implementation of the disclosed subjectmatter.

FIGS. 7A and 7B show example arrangements suitable for beamforming forwireless power transfer according to an implementation of the disclosedsubject matter.

FIG. 8 shows an example arrangement suitable for beamforming forwireless power transfer according to an implementation of the disclosedsubject matter.

FIG. 9 shows an example arrangement suitable for beamforming forwireless power transfer according to an implementation of the disclosedsubject matter.

FIG. 10 shows an example arrangement suitable for beamforming forwireless power transfer according to an implementation of the disclosedsubject matter.

FIG. 11 shows an example procedure suitable for beamforming for wirelesspower transfer according to an implementation of the disclosed subjectmatter.

FIG. 12 shows an example procedure suitable for beamforming for wirelesspower transfer according to an implementation of the disclosed subjectmatter.

FIG. 13 shows an example system suitable for beamforming for wirelesspower transfer according to an implementation of the disclosed subjectmatter.

FIG. 14 shows an example system suitable for beamforming for wirelesspower transfer according to an implementation of the disclosed subjectmatter.

FIG. 15 shows an example system suitable for beamforming for wirelesspower transfer according to an implementation of the disclosed subjectmatter.

FIG. 16 shows an example arrangement suitable for beamforming forwireless power transfer according to an implementation of the disclosedsubject matter.

FIG. 17 shows an example process suitable for beamforming for wirelesspower transfer according to an implementation of the disclosed subjectmatter.

FIG. 18 shows a computer according to an embodiment of the disclosedsubject matter.

FIG. 19 shows a network configuration according to an embodiment of thedisclosed subject matter.

DETAILED DESCRIPTION

According to embodiments disclosed herein, beamforming may be used in awireless power transfer device. The output phase and amplitude of theelements of a wireless power transfer device may be controlled so thatthe waveforms carrying the transmitted energy present a wave front witha coherent phase when they arrive at the elements of the wireless powertransfer device intended to receive the wireless power. The phase andamplitude of the elements of the transmitting wireless power transferdevice may be controlled based on the relative positions of the wirelesspower transfer devices so that the wave front arrives at the receivingwireless power transfer device with a coherent phase regardless of theposition of the receiving wireless power transfer device relative to thetransmitting wireless power transfer device.

Beamforming for wireless power transfer may allow for the output of awireless power transfer device to be controlled to present a coherentphase wave front with uniform amplitude to the elements of a receivingwireless power transfer device. A transmitting wireless power transferdevice may receive a wave front of a beam generated by a receivingwireless power transfer device. The beam may originate with a coherentphase, uniform amplitude wave front generated by the elements of thereceiving wireless power transfer device. The transmitting wirelesspower transfer device may determine the phase and amplitude of the wavefront of the beam as experienced (received) at each element of thetransmitting wireless power transfer device. The transmitting wirelesspower transfer device may generate control signals for its elementsbased on the determined phases of the wave front of the beam asexperienced at its elements, maintaining phase differences across theelements. The control signals may be used to cause each element of thetransmitting wireless power transfer device to transmit a waveform thatis the same as that element's experience of the wave front from thereceiving wireless power transfer device. This may result in thetransmitting wireless power transfer device outputting waveforms thatconstitute a beam that arrives at the elements of the receiving wirelesspower transfer device as a wave front with coherent phase and uniformamplitude.

In some implementations, instead of receiving a wave front of a beamgenerated by the receiving wireless power transfer device beforetransmitting power to the receiving wireless power transfer device, thetransmitting wireless power transfer device may simulate a beam withcoherent phase and uniform amplitude transmitted from the receivingwireless power transfer device. The transmitting wireless power transferdevice may determine the position of the receiving wireless powertransfer device and its elements relative to the transmitting wirelesspower transfer device, including, for example, vertical and horizontaldistance and angle and relative rotation or orientation. Thetransmitting wireless power transfer device may simulate the beam asoriginating from the elements for the receiving wireless power transferdevice with coherent phase and uniform amplitude, and determine thephase and amplitude that would be experienced (received) by the elementsof the transmitting wireless power transfer device upon the arrival ofthe wave front of the simulated beam. The transmitting wireless powertransfer device may generate control signals for its elements based onthe determined phases of the wave front of the simulated beam asexperienced, in simulation, at its elements, maintaining phasedifferences across the elements. The control signals may be used tocause each element of the transmitting wireless power transfer device totransmit a waveform that is the same as that element's experience of thewave front of the simulated beam from the receiving wireless powertransfer device. This may result in the transmitting wireless powertransfer device outputting waveforms that constitute a beam that arrivesat the elements of the receiving wireless power transfer device as awave front with coherent phase and uniform amplitude.

A wireless power transfer device may be any suitable device that may beused for wireless power transfer. For example, a wireless power transferdevice may be an ultrasonic transmitter, which may include a number ofindividual transducer elements. Each transducer element may be aseparate vibrator of any suitable type, such as, for example, apiezoelectric cantilever with a free end and a fixed end. The ultrasonictransmitter may transmit wireless power through ultrasonic wavesgenerated by the transducer elements. The transducer elements of anultrasonic transmitter may be covered with a membrane, which may be anysuitable material for assisting in the translation of the movement ofthe cantilever to movement of the transmission medium, which may be theair. A wireless power transfer device may be a radio frequency (RF)transmitter, which may transmit wireless power using RF waves, or anoptical transmitter which may transmit wireless power using light fromany suitable part of the light spectrum, including, infrared andultraviolet light. A wireless power transfer device may be capable ofsending wireless power, receiving wireless power, sending wirelesscommunications, receiving wireless communications, and performing otherfunctions, such as, for example, imaging and obstacle detection.

Wireless power may be transferred between wireless power transferdevices. For example, a transmitting wireless power device may transferpower to a receiving wireless power transfer device which may providepower to any suitable electronic or electric device, such as asmartphone, laptop, tablet, wearable electronic device, sensor package,electrical motor, or other electrical appliance. The power received bythe wireless power transfer device may be used to directly power adevice, or may be stored, for example, in a battery, capacitor, or anyother suitable form of electrical or power storage. The transmittingwireless power transfer device may draw power from any suitable source,such as, for example, an AC or DC current generated in any suitablemanner, including from a battery, or from an outlet connected to a powergenerator. The efficiency with which wireless power is transmittedbetween a transmitting wireless power transfer device and a receivingwireless power transfer device may be affected by the properties of thewave front that arrives at the elements of the receiving wireless powertransfer device, and the variation in the properties of the wave frontas experienced at those elements. A wave front which presents a coherentphase across the elements of the receiving wireless power transferdevice may improve the efficiency of the transfer of wireless power, asless rectification of the current generated by the received power may beneeded.

A beam originating with a coherent phase may be transmitted from theelements of a receiving wireless power transfer device. The receivingwireless power transfer device may be a target of wireless power from atransmitting wireless power transfer device. For example, the receivingwireless power transfer device may be a smartphone, and the transmittingwireless power transfer device may be a wall panel plugged into anoutlet. The beam may be continuous, or may be pulsed. The beam may betransmitted by causing the elements of the receiving wireless powertransfer device to generate waveforms that are all in phase, resultingin the beam originating with coherent phase. The transmitting wirelesspower transfer device may temporarily halt some or all transmission ofwireless power and enter a receiving mode, for example, based oncommunication from the receiving wireless power transfer deviceindicating the receiving wireless power transfer device is going totransmit to the transmitting wireless power transfer device. Thereceiving wireless power transfer device may transmit the beam for alimited period of time. This may limit the amount of power used by thereceiving wireless power transfer device when it is transmitting. Thismay, for example, avoid draining the battery of an electronic device.

The beam of the wave front transmitted by the receiving wireless powertransfer device may arrive at the elements of the transmitting wirelesspower transfer device. The transmitting wireless power transfer devicemay analyze the properties of the wave front as experienced at eachelement, including the phase and amplitude experienced by each element.The phase and amplitude experienced at the elements of the transmittingwireless power transfer device may vary, for example, due tointerference between the waveforms from the elements of the receivingwireless power transfer device on their route to the transmittingwireless power transfer device. The interference may be influenced bythe relative positions, including locations and orientations, of thetransmitting wireless power transfer device and receiving wireless powertransfer device.

The elements of the transmitting wireless power transfer device maytransmit waveforms based on the elements' experiences of the wave frontfrom the receiving wireless power transfer device. For example, thetransmitting wireless power transfer device may cause the elements totransmit waveforms that have the same phase differences as the elements'experiences of the wave front of the beam transmitted by the receivingwireless power transfer device. Any phase difference between thewaveforms transmitted by any two elements of the transmitting wirelesspower transfer device may be based on the difference between the phasesof the wave front of the beam from the receiving wireless power transferdevice as experienced at the two elements. For example, if a firstelement of the transmitting wireless power transfer device experiencesthe wave front of the beam from the receiving wireless power transferdevice with a phase difference of 15 degrees from a second element ofthe transmitting wireless power transfer device, the waveformtransmitted by the first element may have a phase difference of 15degrees from the waveform transmitted by the second element. Theexperienced phases of the wave front of the beam may result in the beamfrom the transmitting wireless power transfer device having a coherentphase wave front across the elements of the receiving wireless powertransfer device. The beam may also be focused on the receiving wirelesspower transfer device, for example, reducing the amount of power fromthe elements of the transmitting wireless power transfer device thatdoes not reach the receiving wireless power transfer device, forexample, due to being part of the beam that misses the receivingwireless power transfer device.

The amplitude of the waveforms transmitted from the elements of thetransmitting wireless power transfer device may be the same, or may bebased on the amplitude of the wave front from the receiving wirelesspower transfer device as experienced by those elements. For example,elements which experienced a higher amplitude may transmit waveforms ata lower amplitude relative to elements which experienced a loweramplitude, as a phase conjugate of the received waveform normalized to anew power level, or all of the elements may transmit waveforms at thesame amplitude regardless of the amplitude experienced at the element.This may result in the wave front of the beam from the transmittingwireless power transfer device having a uniform amplitude across theelements of the receiving wireless power transfer device.

The beam transmitted from the receiving wireless power transfer devicemay be continuous or may be pulsed, and may be transmitted at anysuitable time or interval. For example, the receiving wireless powertransfer device may transmit the beam originating with coherent phasebefore receiving any wireless power from the transmitting wireless powertransfer device, or once, or at regular intervals while receivingwireless power. The receiving wireless power transfer device maytransmit the beam after communicating with the transmitting wirelesspower transfer device either in-band through the same medium throughwhich wireless power is transferred, or out-of-band, for example, usingany suitable form of wired or wireless communication such as Bluetooth,Wi-Fi, or cellular communication. The communication may indicate to thetransmitting wireless power transfer device that it should temporarilyhalt wireless power transmission to the receiving wireless powertransfer device and prepare to receive the beam transmitted by thereceiving wireless power transfer device. Re-transmitting the beam fromthe receiving wireless power transfer device may allow the phase andamplitude used by the elements of the transmitting wireless powertransfer device to be updated, for example, to account for a change inrelative position between the receiving and transmitting wireless powertransfer devices, or to compensate for localized heating in proximity tothe elements of the receiving wireless power transfer device that mayresult from absorption of the wave front and form a gas lens effect.

In some implementations, the transmitting wireless power transfer devicemay simulate the beam originating with a coherent phase from thereceiving wireless power transfer device. The simulation of the beam maybe based on the position of the receiving wireless power transfer devicerelative to the transmitting wireless power transfer device. Thetransmitting wireless power transfer device may determine the positionof the receiving wireless power transfer device in any suitable manner.For example, the transmitting wireless power transfer device mayrequest, or receive without requesting, position data from the receivingwireless power transfer device, such as, for example, accelerometer orgyroscope data, which may indicate the orientation of the receivingwireless power transfer device relative to the transmitting wirelesspower transfer device. Any suitable form of range finding may be used todetermine the distance between the receiving wireless power transferdevice and the transmitting wireless power transfer device. For example,elements of the transmitting wireless power transfer device may transmitwaveforms at a given time. The receiving wireless power transfer devicemay receive the waveforms, and may send an indication of the time atwhich the waveforms were received to the transmitting wireless powertransfer device using any suitable form of communication. Thetime-of-flight of the waveforms between the transmitting and receivingwireless power transfer devices and the type of wireless power transfermay be used to determine the distance between transmitting and receivingwireless power transfer devices. The transmitting wireless powertransfer device may sweep the transmission of a beam over a given area,for example, using pulsed transmission at various angles, until thereceiving wireless power transfer device indicates it received the beam,allowing for the determination of the direction of the receivingwireless power transfer device relative to the transmitting wirelesspower transfer device. The position of the receiving wireless powertransfer device may also be determined by, for example, separatetracking or range-finding devices on either or both of the transmittingand receiving wireless power transfer devices. The position of thereceiving wireless power transfer device may include the positions andorientations of elements on the receiving wireless power transferdevice.

The transmitting wireless power transfer device may simulate the beamand its wave front in any suitable manner. For example, the transmittingwireless power transfer device may simulate a waveform transmitted fromeach element of the receiving wireless power transfer device. The beammay be simulated as being continuous or pulsed. The simulated waveformsmay be simulated as having coherent phase at their origin. Thetransmitting wireless power transfer device may simulate the propagationof the waveforms from each element of the receiving wireless powertransfer device, including any interference between the waveforms asthey propagate away from the receiving wireless power transfer device.The simulation may be based on, for example, the type of wireless powertransfer being used and the medium through which the waveforms travel,and may attempt to account for losses of amplitude during propagation.For example, if ultrasonic waves are used to transfer wireless power,the simulated waveforms may be simulated traveling through the air, andthe simulation may account for the temperature and density of the air,for example, as determined by a thermometer and barometer of thetransmitting or receiving wireless power transfer devices. Thesimulation may attempt to account for any loss in amplitude of theultrasonic waves between the receiving and transmitting wireless powertransfer devices due to transfer of energy to the air. The simulationmay also account for the relative of position of the elements of thereceiving wireless power transfer device and the directivity ofwaveforms generated by the elements. For example, the elements may bearranged in any suitable configuration, and may be arranged on anynumber of flat or curved planes of any suitable type. For example, theelements of the receiving wireless power transmitter may be arranged onthe curved back of a smartphone, such that waveforms generated by theelements may not be directed in the same direction.

Simulating the interference between waveforms originating at theelements of the receiving wireless power transfer device with coherentphase and propagating away from the receiving wireless power transferdevice may result in the simulation of a beam with a wave front arrivingat the elements of the transmitting wireless power transfer device.Simulation of the waveforms may be performed until the simulatedwaveforms have reached a distance from the receiving wireless powertransfer device that is equal to the distance between the transmittingand receiving wireless power transfer devices, indicating that thewaveforms have been simulated up to their arrival at the elements of thetransmitting wireless power transfer device. The simulation may beperformed with any suitable level of granularity. For example, thesimulation may simulate the waveforms from the receiving wireless powertransfer device to the transmitting wireless power transfer device atregular intervals of 1/100000 of a second. The simulation may stop witha simulated wave front, resulting from the simulated waveforms, that hasreached all of the elements of the transmitting wireless power transferdevice that can be reached by the wave front based on their relativepositions. The transmitting wireless power transfer device may determinehow each element of the transmitting wireless power transfer devicewould experience the simulated wave front resulting from the simulatedwaveforms, based on the properties of the simulated wave front at thepositions of the elements of the transmitting wireless power transferdevice. The transmitting wireless power transfer device may, forexample, determine the phase and amplitude of the simulated wave frontat the position of each element of the transmitting wireless powertransfer device. The simulation may also be performed based on anysuitable calculation or approximation which may determine the propertiesof the simulated wave front as it would be experienced on arrival at theelements of the transmitting wireless power transfer device based on theproperties of the waveforms originating at the elements of the receivingwireless power transfer device. The calculation or approximation mayallow for simulation of the waveforms, and the wave front, as it travelsbetween the receiving wireless power transfer device and thetransmitting wireless power transfer device to be skipped. The wavefront at the elements of the transmitting wireless power transfer devicemay be determined directly from the properties of the wave front at itsorigin at the receiving wireless power transfer device. This may allowfor faster determination of the properties of the simulated wave frontat the elements of the transmitting wireless power transfer device andfaster determination of waveforms that should be transmitted by theelements of the transmitting wireless power transfer device, allowingfor the transmitting wireless power transfer device to alter its beam tokeep up with changes in the relative positioning of the transmitting andreceiving wireless power transfer devices.

The elements of the transmitting wireless power transfer device maytransmit waveforms that are the same as the elements' simulatedexperiences of the wave front of the simulated beam from the receivingwireless power transfer device. For example, the transmitting wirelesspower transfer device may cause the elements to transmit have the samephase differences as the elements' simulated experiences of the wavefront of the simulated beam. Any phase difference between the waveformstransmitted by any two elements of the transmitting wireless powertransfer device may be based on the difference between the phases of thewave front of the simulated beam as experienced in simulation at the twoelements. For example, if a first element of the transmitting wirelesspower transfer device experiences the wave front of the same with aphase difference of 15 degrees from a second element of the transmittingwireless power transfer device, the waveform transmitted by the firstelement may have phase difference of 15 degrees from the waveformtransmitted by the second element. Transmitting waveforms using theexperienced phases of the wave front of the simulated beam may result inthe beam from the transmitting wireless power transfer device having acoherent phase wave front across the elements of the receiving wirelesspower transfer device. The beam may also be focused on the receivingwireless power transfer device, for example, reducing the amount ofpower from the elements of the transmitting wireless power transferdevice that does not reach the receiving wireless power transfer device,for example, due to being part of the beam that misses the receivingwireless power transfer device.

The amplitude of the waveforms transmitted from the elements of thetransmitting wireless power transfer device may be the same, or may bebased on the amplitude of the wave front of the simulated beam asexperienced in simulation by those elements. For example, elements whichexperienced a higher amplitude in simulation may transmit waveforms at alower amplitude relative to elements which experienced a lower amplitudein simulation, as a phase conjugate of the received waveform normalizedto a new power level, or all of the elements may transmit waveforms atthe same amplitude regardless of the amplitude experienced at theelement in simulation. This may result in the wave front of the beamfrom the transmitting wireless power transfer device having a uniformamplitude across the elements of the receiving wireless power transferdevice.

Simulation of the beam originating at the receiving wireless powertransfer device may be performed at any suitable time, and may berepeated at any suitable intervals. For example, the simulation may befirst performed based on a communication from the receiving wirelesspower transfer device requesting wireless power from the transmittingwireless power transfer device. The transmitting wireless power transferdevice may perform the simulation of the beam, and then may begintransmitting wireless power to the receiving wireless power transferdevice based on the results of the simulation. The transmitting wirelesspower transfer device may perform the simulation of the beam again atany suitable intervals. For example, the simulation may be performed ona regular update cycle, based on detecting that the position of thereceiving wireless power transfer device relative to the transmittingwireless power transfer device has changed, or based on communicationsfrom the receiving wireless power transfer device which may indicate,for example, that the receiving wireless power transfer device requiresmore or less power or has moved, or may include feedback indicating thephase and amplitude of the wave front of the beam from the transmittingwireless power transfer device as experienced at the receiving wirelesspower transfer device.

The experience of the wave front of the simulated beam may be simulatedin parallel for the elements of the transmitting wireless power transferdevice. The experience of the wave front of the simulated beam by anyindividual element of the transmitting wireless power transfer devicemay be simulated independently of the experience of the wave front ofthe simulated beam by any other individual element of the transmittingwireless power transfer device. For example, the relative Euclideandistance and angle between an element of the transmitting wireless powertransfer device and each element of the receiving wireless powertransfer device for which a waveform is being simulated may be used todetermine the properties, including relative phase, amplitude, anddirectivity, of the wave front of the simulated beam as it would beexperienced at the element of the transmitting wireless power transferdevice. This determination may made independently for each element ofthe transmitting wireless power transfer device, which may allow theproperties of the wave front of the simulated beam as experienced ateach element of the wireless power transfer device to be determined viasimulation in parallel.

In some implementations, the simulation may determine the experience ofthe wave front of the simulated beam at a subset of the elements of thetransmitting wireless power transfer device. For example, the simulationmay determine how a uniform sample of elements, for example, everysecond element, or a random sample of elements, of the transmittingwireless power transfer device would experience the wave front of thesimulated beam originating at the elements of the receiving wirelesspower transfer device. Elements for which the experience of the wavefront of the simulated beam is not simulated may transmit with a phaseand amplitude that is based on the phase and amplitude used byneighboring or nearby elements for which the experience of the wavefront of the simulated beam was simulated. For example, an element forwhich no simulation was performed may transmit using the same phase andamplitude as the nearest element for which a simulation was performed, amodified phase and amplitude based on the phase and amplitude used bythe nearest element for which a simulation was performed, or a phase andamplitude that is an average of, or based on an interpolation of,several neighboring or nearby elements for which a simulation wasperformed. Further simulations may be performed, for example, atsuitable intervals, such as on a regular update cycle, which maysimulate elements of the transmitting wireless power transfer device forwhich simulations were not previously performed. This may allow forfurther focusing of the beam from the transmitting wireless powertransfer device, resulting in a more coherent phase wave front beingexperienced across the elements of the receiving wireless power transferdevice. As simulation of the experience of the wave front of thesimulated beam is performed for additional elements, those elements maybegin to transmit waveforms based on the result of the simulationinstead of waveforms copied from neighbors or based on interpolation.New simulations may also be performed for elements for which simulationswere previously performed.

In some implementations, the simulation may simulate the beam from thereceiving wireless power transfer device as originating at a subset ofthe elements of the receiving wireless power transfer device. The subsetof the elements of the receiving wireless power transfer device fromwhich the beam is simulated may be arranged in any suitable manner. Forexample, a receiving wireless power transfer device may include elementsarranged in rectangular grid that is 20 elements tall by 10 elementswide. The simulation may simulate waveforms from a bottom 100 elementsof the grid of elements. The wave front of the simulated beamexperienced at the elements of the transmitting wireless power transferdevice may be the product of the simulated waveforms from the bottom 100elements. The wave front resulting from waveforms transmitted by theelements of the transmitting wireless power transfer device based on theexperience of the wave front of the simulated beam may have a coherentphase over the 100 elements of the receiving wireless power transferdevice for which waveforms were simulated, and may have less phasecoherence over the 100 elements for which waveforms were not simulated.Subsequent simulations may be performed to simulate waveforms for the100 elements of the receiving wireless power transfer device for whichwaveforms were not previously simulated. The elements of thetransmitting wireless power transfer device may experience, insimulation, the wave front of the simulated beam resulting from thesimulated waveforms originating at the 100 elements of the receivingwireless power transfer device for which waveforms were not previouslysimulated. The phase of the wave front of the simulated beam experiencedby an element of the transmitting wireless power transfer device may beadded to the phase of the previously simulated wave front experienced bythe element. This may update the phase of the wave front of thesimulated beam as experienced at the element to account for all of theelements of the receiving wireless power transfer device for whichwaveforms have been simulated, even when they were simulated duringdifferent update cycles. This may result in the wave front of the beamfrom the transmitting wireless power transfer device having coherentphase over the 200 elements of the receiving wireless power transferdevice.

In some implementations, the beam may be simulated with waveformsoriginating at points on the receiving wireless power transfer devicethat do not correspond to the location of elements. The waveforms may besimulated from any suitable number of points. For example, a waveformmay be simulated as originating from the center of mass of the receivingwireless power transfer device, forming the beam. The waveforms may besimulated as originating from points located in between elements of thereceiving wireless power transfer device. For example, if the elementsare arranged in a grid, the waveforms may be simulated as originatingfrom points on the grid where the corners of four elements meet, formingthe beam. The simulated waveforms may be simulated as originating fromany suitable number of points at any suitable locations on the receivingwireless power transfer device. In some implementations, a firstsimulation may simulate waveforms originating from a point or points onthe receiving wireless power transfer device, and simulations onsubsequent update cycles may simulate waveforms originating fromelements of the receiving wireless power transfer device.

Simulating the wave front as originating at a subset of elements of, orfrom a point or points on, the receiving wireless power transfer devicemay allow for the simulation to be completed more quickly, using fewercomputational resources. This may result in the transmission of power tothe receiving wireless power transfer device commencing sooner than itwould have had waveforms been simulated for all of the elements of thereceiving wireless power transfer device, or at a larger number ofpoints, although the efficiency of the power transfer may be lower. Tocompensate for lower efficiency while waveforms have not yet beensimulated from all of the elements of the receiving wireless powertransfer device, the transmitting wireless power transfer device maytransmit using more elements, and may also transmit at a higheramplitude. As waveforms are simulated from more of the elements, or frommore points, of the receiving wireless power transfer device, the beamtransmitted by the transmitting wireless power transfer device mayincrease in phase coherence across the elements of the receivingwireless power transfer device. This may increase the efficiency of thepower transfer, allowing the transmitting wireless power transfer deviceto transmit using fewer elements and to reduce the amplitude of theelements being used.

For example, before beginning to transmit power to a receiving wirelesspower transfer device, a waveform originating from the center of mass ofthe receiving wireless power transfer device may be simulated. Theexperience, in simulation, by the elements of the transmitting wirelesspower transfer device of the wave front of the simulated beamconstituted by the simulated waveform may be determined. The experiencedphases may be used to determine the phases used by the elements of thetransmitting wireless power transfer device as they begin transmitting,transferring power to the receiving wireless power transfer device. Asthe simulation only used the center of mass of the receiving wirelesspower transfer device, the beam from the transmitting wireless powertransfer device may be focused on the center of mass of the receivingwireless power transfer device. This may result in the elements of thereceiving wireless power transfer device experiencing the wave front ofthe beam with varying phases, resulting in less efficient powertransfer. During subsequent update cycles, waveforms may be simulatedfrom additional points on, or from elements of, the receiving wirelesspower transfer device. This may result in updates to the phases used bythe elements of the transmitting wireless power transfer device. Asadditional waveforms are simulated from additional points or elements,the wave front of the beam transmitted by the transmitting wirelesspower transfer device may increase in phase coherence across theelements of the receiving wireless power transfer device, resulting inan increase in the efficiency of the power transfer.

Simulations of waveforms from elements of the receiving wireless powertransfer device, or other points of the receiving wireless powertransfer device, may be performed in any suitable order, for anygroupings of elements and points over any number of intervals or updatecycles. For example, half of the elements of a receiving wireless powertransfer device may have waveforms simulated in a first cycle, and halfof the remaining elements may have waveforms simulated in eachsubsequent update cycle, such that fewer elements have waveformssimulated in each update cycle until all elements have had waveformssimulated. Elements or points for which waveforms were simulated in aprevious update cycle may have waveforms simulated in a subsequentupdate cycle, for example, to account for a change in relative positionbetween the transmitting and receiving wireless power transfer devices.

In some implementations, instead of a first simulation, the elements ofthe transmitting wireless power transfer device may begin transmittingusing phases based on an approximation derived from pre-computed tablesor phase patterns which may be defined through analytic approximationsthat may describe the qualitative evolution of the focusing profile,including the phases to be used by the elements of the transmittingwireless power transfer device, through different angles and distances.This may allow the elements of the transmitting wireless power transferdevice to quickly begin transmitting with a focus on the receivingwireless power transfer device. To offset any inefficiencies in thepower transfer due to the use of an approximation to determine thephases used by the elements of the transmitting wireless power transferdevice, more elements may be used, and the elements may transmit athigher amplitudes. Subsequent update cycles may simulate waveforms fromelements of or points on the receiving wireless power transfer device,resulting in updates to the phases used by the elements of thetransmitting wireless power transfer device. This may result inincreased phase coherence of the wave front across the elements of thereceiving wireless power transfer device. The transmitting wirelesspower transfer device may be able to transmit power using fewerelements, at lower amplitudes, as the efficiency of the power transferincreases. The amplitude of the waveforms transmitted from the elementsof the transmitting wireless power transfer device may be based on theapproximation used in lieu of the first simulation, and may be updatedas simulations are performed.

In some implementations, instead of simulating a wave front that has acoherent phase, or flat phase, at its origin at the receiving wirelesspower transfer device, a wave front with a defined phase pattern may besimulated. This may allow for optimization of the waveforms, andresulting wave front, transmitted by the transmitting wireless powertransfer device for specific groupings of elements on the receivingwireless power transfer device or for time uniformity of therectification used by the receiving wireless power transfer device torectify the electric current generated by its elements based on thetransferred power. For example, two subsets of elements of the receivingwireless power transfer device, covering two separate areas, may havetheir simulated waveforms 90 degrees out-of-phase. This may result inthe beam from the transmitting wireless power transfer device,transmitted based on the simulated waveforms, being 90 degreesout-of-phase across the two subsets of elements of the receivingwireless power transfer device. For example, the second subset ofelements of the receiving wireless power transfer device may experiencethe wave front of the beam from the transmitting wireless power transferdevice with a phase 90 degrees behind the first subset of elements. Thismay allow the receiving wireless power transfer device to keep power inits rectification through nulls in the wave front experienced by thefirst subset of elements and the second subset of elements, as one ofthe subsets of elements will be generating current from the powertransferred by the wave front while the other is in a null due to thephase difference. The elements of the receiving wireless power transferdevice may be divided into any number of subsets, with any number ofphase differences of any suitable size between the subsets. This mayallow drops in the rectified electrical signal to be smoothed outthrough the different phases the wave front of the beam from thetransmitting wireless power transfer device presents to the subsets ofelements of the receiving wireless power transfer device.

In some implementations, the phases and amplitudes to be transmitted bythe elements of the transmitting wireless power transfer device may bedetermined by analyzing spatial frequencies of a wave front of a beamoriginating at the receiving wireless power transfer device usingFourier transforms. The analysis may determine the phases and amplitudesof a diffraction field at any coplanar offset from the receivingwireless power transfer device, such as, for example, at the location ofthe elements of the transmitting wireless power transfer device. Anestimate of the angular misalign of the planes of the receiving wirelesspower transfer device and the transmitting wireless power transferdevice may be incorporated into the analysis through small angleprojections if the planes are not parallel.

The receiving wireless power transfer device may be treated as adiffracting aperture projecting onto the plane of the transmittingwireless power transfer device. The resulting diffraction pattern maydefine the phases and amplitudes that would be observed or experiencedin the plane of the transmitting wireless power transfer device,including at the elements of the transmitting wireless power transferdevice, as a phase/amplitude map. The positions on the plane thatcorrespond to the elements of the transmitting wireless power transferdevice may be sampled from the diffraction pattern, or phase/amplitudemap, as determined using Fourier transforms. The phase conjugate may beapplied to the sampled parts of the diffraction pattern to determine aphase/amplitude map, or phase and amplitude profile, which may be usedby the transmitting wireless power transfer device to determine thephases and amplitudes that may be used by the elements of thetransmitting wireless power transfer device to generate a beam with auniform phase and amplitude wave front at the elements of the receivingwireless power transfer device.

The amplitudes used by the elements of the transmitting wireless powertransfer device may be renormalized to the maximum power point of theelements of the transmitting wireless power transfer device to optimizethe total power being transmitted. A lower power point may also bechosen for renormalization. The total power transmitted from thetransmitting wireless power transfer device may be divided over multiplereceiving wireless power transfer devices. This may be accomplishedthrough the complex addition of multiple diffraction patterns, orphase/amplitude maps, and normalization to the maximum power that can beaccomplished by any single element of the transmitting wireless powertransfer device.

A wave front of uniform amplitude and phase may be defined in the planeof an aperture of the receiving wireless power transfer device. Theaperture may correspond to the area encompassed by all, or a subset of,the elements of the receiving wireless power transfer device. The pitchof samples taken on the plane of the aperture of the receiving wirelesspower transfer device may correspond with any of the element pitch onthe transmitting wireless power transfer device, the element pitch onthe receiving wireless power transfer device, the greatest commonmultiple of the pitch of the elements of the transmitting wireless powertransfer device and receiving wireless power transfer device, and anyconvenient or suitable pitch that may be interpolated from and onto theelements of the aperture of the receiving wireless power transfer deviceand the elements of an aperture of the transmitting wireless powertransfer device.

If the plane of the aperture of the receiving wireless power transferdevice is not parallel to the plane of the aperture of the transmittingwireless power transfer device, phase corrections may be determined thatmay be applied to each element of the aperture of the receiving wirelesspower transfer device to make the aperture of the receiving wirelesspower transfer device quasi-parallel to the plane of the aperture of thetransmitting wireless power transfer device. For example, a first-orderapproximation may be made that the apparent width of the aperture of thetransmitting wireless power transfer device remains constant from theperspective of the plane (P₂) of the aperture of the receiving wirelesspower transfer device, for example, as a square aperture driven withequal amplitude across its face. If the receiving wireless powertransfer device has a flat phase profile across its surface theresulting phase profile, as part of a phase/amplitude map, in theparallel plane, for example, the plane (P₁) of the aperture of thetransmitting wireless power transfer device, may be calculated bynormalizing the receiving wireless power transfer device's actualsurface normal unit vector {right arrow over (n_(r))} to length

${\overset{\rightarrow}{k}} = \frac{2\pi}{\lambda}$

and taking it to be the central {right arrow over (k)} of the emittedangular spectrum from the aperture of the receiving wireless powertransfer device, where λ is the wavelength of the plane wave associatedwith the vector {right arrow over (k)}, which may be normal to the planewave. The phase profile of the phase/amplitude map at the plane P₂ maybe approximately given by:

ϕ_(r)(x,y)=e ^(−i(k) ^(rx) ^(x+k) ^(ry) ^(y))  (1)

where

{right arrow over (k _(r))}=

k _(rx) ,k _(ry) ,k _(rz)

=|{right arrow over (k)}|·{right arrow over (n _(r))}  (2)

This may be a rotation of a true flat phase profile of the aperture ofthe receiving wireless power transfer device to give a notional emittedfield, or wave front, represented by the phase/amplitude map r_(xE)(x,y) a linear phase profile in the plane P₂ by multiplication by a complexexponential. This may be a shift of the angular spectrum in spatialfrequency to be centered around (v_(rx), v_(ry))=(k_(rx), k_(ry))/2π.Similarly, after r_(xR)(x, y), which may be a phase/amplitude map for aphysical field, or wave front, received at the elements of the apertureof the receiving wireless power transfer device, is calculated in theplane P₂, it may be rotated back into the plane of the aperture of thereceiving wireless power transfer device by division by the same complexexponential.

A Fourier transform in the plane P₂ of the aperture of the receivingwireless power transfer device may be determined, resulting in a spatialfrequency representation in the plane P₂. r_(xE)(x, y) may be aphase/amplitude map for the notional field that would emitted from theaperture of the receiving wireless power transfer device, for example,based on the elements of the receiving wireless power transfer devicetransmitting waves, such as ultrasonic waves, with uniform phase andamplitude. A Fourier transform may be used to determine R_(xE)(v_(x),v_(y)), which may be the Fourier transform of r_(xE)(x, y), and may bethe spatial frequency representation in the plane P₂ of the notionalfield, or wave front, that would be emitted from the aperture of thereceiving wireless power transfer device based on the phase/amplitudemap r_(xE)(x, y).

The notional field r_(xE), with the phase/amplitude map r_(xE)(x, y),may be propagated from the plane P₂ of the aperture of the receivingwireless power transfer device to the plane P₁ of the aperture of thetransmitting wireless power transfer device in the spatial frequencydomain. t_(xR)(x, y) may be a phase/amplitude map for a notional fieldthat would be received at the aperture of the transmitting wirelesspower transfer device based on r_(xE)(x, y) being emitted from theaperture of the receiving wireless power transfer device. t_(xR)(x, y)may be determined according to:

T _(xR)(v _(x) ,v _(y))=R _(xE)(v _(x) ,v _(y))H(v _(x) ,v _(y))  (3)

where T_(xR)(v_(x), v_(y)) is the Fourier Transform of t_(xR)(x, y), andwhere:

H(v _(x) ,v _(y))=e ^(jk) ^(z) ^(d)  (4)

where

${j = \sqrt{- 1}},{k_{z} = {2\pi \sqrt{\frac{1}{\lambda^{2}} - v_{x} - v_{y}}}},$

λ is the wavelength of the plane wave associated with the vector {rightarrow over (k)}, which may be normal to the plane wave, and d is thedisplacement on the z-axis between the plane P₂ and the plane P₁, where{right arrow over (k)}(v_(x), v_(y))=

k_(x), k_(y), k_(z)

, with v_(x) and v_(y) being transverse spatial frequencies in theplane. Additionally, k_(x)=2πv_(x) and k_(y)=2πv_(y). The magnitude ofthe plane wave associated with the vector

$\overset{\rightarrow}{k} = {k = {\frac{2\pi}{\lambda}.}}$

T_(xR)(v_(x), v_(y))=R_(xE)(v_(x), v_(y))H(v_(x), v_(y)) may beequivalent to t_(xR)(x, y)=r_(xE)(x, y)*h(x, y), where the * operatormay represent linear convolution. This may be used to determine anyfield in the plane z=d, or f(x, y, z=d)=g(x, y) based on the field inany plane f(x, y, z=0)=f(x, y) according to G(v_(x), v_(y))=F(v_(x),v_(y))H(v_(x), v_(y)) or g(x, y)=f(x, y)*h(x, y) where to G(v_(x),v_(y)) is a Fourier transform of g(x, y) and F(v_(x), v_(y)) is aFourier transform of f(x, y).

H(v_(x), v_(y)) may be a transformation kernel, or spatial-frequencydomain transfer function, that may define the Fourier transform of thepoint spread function for Fraunhofer diffraction at the orthonormaldistance between the plane of the aperture of the transmitting wirelesspower transfer device and the center point of the aperture of thereceiving wireless power transfer device.

H(v_(x), v_(y)) may be applied to the Fourier transform R_(xE)(v_(x),v_(y)), which may be the spatial frequency representation of the planeof the aperture of the receiving wireless power transfer device. Aninverse Fourier transform may be applied to the result T_(xR)(v_(x),v_(y)), which may be the spatial frequency representation of the planeof the aperture of the transmitting wireless power transfer device, toproduce t_(xR)(x, y), which may be the phase/amplitude map of the planeof the aperture of the transmitting wireless power transfer device.

The spatial diffraction pattern, or phase/amplitude map, t_(xR)(x, y)may be windowed to the aperture of the transmitting wireless powertransfer device and a phase conjugate may be applied to the complexamplitude/phase signal to determine the phase/amplitude map that mayreconstruct the notional field represented by the phase/amplitude mapr_(xE)(x, y) at the aperture of the receiving wireless power transferdevice. Resampling of the phase/amplitude map t_(xR)(x, y) may benecessary if the pitch of the constructed plane of the aperture of thereceiving wireless power transfer device does not correspond to theelement pitch of the transmitting wireless power transfer device.

For example, t_(xE)(x, y) may be the phase/amplitude map of the physicalfield emitted by elements of the transmitting wireless power transferdevice, for example, as an ultrasonic beam, intended to produce thedesired complex field in the plane of the aperture of the receivingwireless power transfer device. t_(xE)(x, y) may be determined in thespatial domain according to:

t _(xE)(x,y)=t _(xR)*(x,y)A _(tx)(x,y)  (5)

where t_(xR)*(x, y) is the complex conjugate of t_(xR)(x, y), andA_(tx)(x, y) is the aperture of the transmitting wireless power transferdevice, as only the portion of t_(xR)(x, y) which overlaps the apertureof the transmitting wireless power transfer device may be physicallyphase-conjugated and re-radiated by the elements of the transmittingwireless power transfer device.

The magnitude of the phase/amplitude map t_(xE)(x, y) may be normalizedto optimize the desired power level transmitted from the transmittingwireless power transfer device. This may include maximizing the powertransmitted by the transmitting wireless power transfer device, tuningto a particular desired power level, for example, as indicated by thereceiving wireless power transfer device, and dividing the totalavailable power of the transmitting wireless power transfer device overmultiple receiving wireless power transfer devices. Apertures may becombined through linear superposition. Normalization and prediction ofpower delivered may be determined prior to or after the combination ofapertures depending upon the result desired.

r_(xR)(x, y) may be the phase/amplitude map of the physical fieldreceived in the plane of the aperture of the receiving wireless powertransfer device, for example, as the wave front of an ultrasonic beamfrom the elements of the transmitting wireless power transfer device.When the transmitting wireless power transfer devices emits a physicalfield, such as the ultrasonic beam, based on the phase/amplitude mapt_(xE)(x, y), the field r_(xR)(x, y) may be predicted by:

R _(xR)(v _(x) ,v _(y))=T _(xE)(v _(x) ,v _(y))H(v _(x) ,v _(y))  (6)

where T_(xE)(v_(x), v_(y)) is the Fourier transform of t_(xE)(x, y) andR_(xR)(v_(x), v_(y)) is the Fourier transform of r_(xR)(x, y).

Zero padding prior to the use of Fourier transformation may be used toallow the desired linear convolution to be extracted from the circularconvolution implemented by multiplication in the discrete spatialfrequency domain. This may result in a sampled region that is largerthan the face of the array of elements of the transmitting wirelesspower transfer device. When the diffraction pattern is located near thecenter of the array of elements of the transmitting wireless powertransfer device, less zero padding may be used. For example, when thetransmitting wireless power transfer device includes an array ofelements that is 160 elements x 160 elements, zero padding may be usedto create a sample space that may be 1024 elements x 1024 elements. Whenthe portion of interest of the diffraction pattern lies farther from thecenter of the array of elements of the transmitting wireless powertransfer device, for example, due to the plane of the aperture of thereceiving wireless power transfer device being at a steep angle to theplane of the aperture of the transmitting wireless power transferdevice, more zero padding may be used.

The power coupling efficiency η between the notional field emitted bythe receiving wireless power transfer device, r_(xE), and the physicalfield received by the receiving wireless power transfer device, r_(xR),may be evaluated by an overlap integral over an infinite plane in spaceaccording to:

$\begin{matrix}{{\eta \left( {r_{xE},r_{xR}} \right)} = \frac{{{\int{r_{xE}^{*}r_{xR}{dA}}}}^{2}}{\int{{r_{xE}}^{2}{dA}{r_{xR}}^{2}{dA}}}} & (7)\end{matrix}$

Since r_(xE) may have a value of 0 at any location in space that is notpart of the aperture of the receiving wireless power transfer device,the integral may be evaluated over the area of the aperture of thereceiving wireless power transfer device. Because the physical fieldt_(xE) and the notional field t_(xR) may be free space propagations ofthe notional field r_(xE) and the physical field r_(xR), power couplingefficiency may be determined immediately in the plane of the aperture ofthe transmitting wireless power transfer device, as η(r_(xE),r_(xR))=η(t_(xE), t_(xR)), where the areas of integration are the areasof the apertures of the transmitting and receiving wireless powertransfer devices.

Optimal power transfer between the transmitting wireless power transferdevice and the receiving wireless power transfer device may occur whenthe field emitted from the transmitting wireless power transfer deviceis the phase conjugate of the complete diffraction pattern produced onthe plane of the transmitting wireless power transfer device by thenotional field with the flat phase/amplitude map emitted notionally bythe receiving wireless power transfer device. When the entire phaseconjugate diffraction pattern cannot be generated, only the portion ofthe generated field that overlaps with the diffraction pattern may enterthe mode of the receiving wireless power transfer device. If themajority of the diffraction pattern intensity produced on the plane ofthe transmitting wireless power transfer device by the flatphase/amplitude map at the receiving wireless power transfer device doesnot land within the aperture of the transmitting wireless power transferdevice, power may not be efficiently coupled in either direction. Anoptimum phase/amplitude map may maximize the fraction of energy in thediffraction pattern of the receiving wireless power transfer device thatlands within the aperture of the transmitting wireless power transferdevice.

The receiving wireless power transfer device may provide feedback to thetransmitting wireless power transfer device. The feedback may beprovided using any suitable form of communication. For example, thecommunication may be in-band, using the elements of the receivingwireless power transfer device to transmit data to the elements of thetransmitting wireless power transfer device, or out-of-band, using, forexample, Bluetooth, Wi-Fi or cellular communications, or any othersuitable form of wireless or wired communication. The feedback from thereceiving wireless power transfer device may indicate the phase andamplitude of the wave front of the beam formed by the waveforms from theelements of the transmitting wireless power transfer device as measuredat the elements of the receiving wireless power transfer device. Thetransmitting wireless power transfer device may use the feedback toadjust the phases and amplitudes used by its elements, for example, toreduce any unintentional phase incoherence across the elements of thereceiving wireless power transfer device as indicated by the feedback.The feedback may also indicate to the transmitting wireless powertransfer device that the receiving wireless power transfer devicerequires less power, for example, due to a battery being charged to somethreshold level. The transmitting wireless power transfer device maychange the phase and amplitude used by its elements, and the number ofelements used, so that the transferred power can be used to tricklecharge the battery of the receiving wireless power transfer device. Thephases and amplitudes used may be chosen for efficiency, rather than formaximum power transfer or for maintaining a coherent phase wave frontacross the elements of the receiving wireless power transfer device.

FIG. 1 shows an example system suitable for beamforming for wirelesspower transfer according to an implementation of the disclosed subjectmatter. A transmitting wireless power transfer device 100 may includeelements 111, 112, 113, 114, 115, 116, 117, 118, and 119, which may becapable of transmitting and receiving wireless power. The transmittingwireless power transfer device 100 may be a device for transmittingwireless power, which may draw power from a source of energy such as apower outlet connected to any suitable power source, a battery, or anyother source of energy, and may be designed to provide power to otherelectronic or electric devices. The elements 111, 112, 113, 114, 115,116, 117, 118, and 119 may be, for example, ultrasonic transducerelements, RF transducer elements, optical transducer elements, or anyother element type suitable for the transmission of wireless power. Theelements 111, 112, 113, 114, 115, 116, 117, 118, and 119 may be capableof operating in both a transmitting and receiving mode. In atransmitting mode, the elements 111, 112, 113, 114, 115, 116, 117, 118,and 119 may generate waveforms, for example, ultrasonic sound waves, RFwaves, or light waves, which may carry energy to a receiving wirelesspower transfer device 150. In a receiving mode, the elements 111, 112,113, 114, 115, 116, 117, 118, and 119 may react to receiving waveforms,for example, ultrasonic sound waves, RF waves, or light waves generatedelsewhere by converting the waveforms into electrical signals. Forexample, an ultrasonic transducer may use a piezoelectric flexure whichmay vibrate at ultrasonic frequencies when an appropriate electricalsignal is supplied, generating an ultrasonic sound wave, and may bevibrated at ultrasonic frequencies when receiving an ultrasonic soundwave, generating an electrical signal. In some implementations, theelements 111, 112, 113, 114, 115, 116, 117, 118, and 119 may beoptimized for the transmitting of wireless power.

A receiving wireless power transfer device 150 may include elements 151,152, 153, 154, 155, 156, 157, 158, and 159, which may be capable ofreceiving and transmitting wireless power. The receiving wireless powertransfer device 150 may be a component of, or connected to, anelectronic or electric device to which the receiving wireless powertransfer device 150 may supply power. For example, the receivingwireless power transfer device 150 may be part of a smartphone, and maysupply electricity to the smartphone's battery. The elements 151, 152,153, 154, 155, 156, 157, 158, and 159 may be, for example, ultrasonictransducer elements, RF transducer elements, optical transducerelements, or any other element type suitable for the transmission ofwireless power. The elements 151, 152, 153, 154, 155, 156, 157, 158, and159 may be of the same type, or of a similar type with optimizations forthe specific role of the element, as the elements 111, 112, 113, 114,115, 116, 117, 118, and 119, in order to allow the transfer of wirelesspower between the transmitting wireless power transfer device 100 andthe receiving wireless power transfer device 150. For example, anelement of the wireless power transfer device 100 may be optimized forpower transmission, while an element of the receiving wireless powertransfer device 150 may be optimized for power receiving.

The elements 111, 112, 113, 114, 115, 116, 117, 118, and 119 maygenerate waveforms, for example, based on received electrical signals.The waveforms may form a beam 180, carrying energy to the receivingwireless power transfer device 150. The beam 180 may be, for example, abeam of ultrasonic sound waves, RF waves, or light. A wave front of thebeam 180 may arrive at the elements 151, 152, 153, 154, 155, 156, 157,158, and 159, resulting in the generation of electricity by thereceiving wireless power transfer device 150 from the energy carried bythe beam 180. The efficiency with which the receiving wireless powertransfer device 150 generates electricity from the beam 180 may dependon, for example, whether the beam 180 is directed at the receivingwireless power transfer device 150, how focused the beam is on thereceiving wireless power transfer device 150, and the phase coherence ofthe wave front of the beam 180 across the elements 151, 152, 153, 154,155, 156, 157, 158, and 159. The transmitting wireless power transferdevice 100 may control the steering and focus of the beam 180 and thephase of the wave front across the elements 151, 152, 153, 154, 155,156, 157, 158, and 159 by controlling the phases of the waveformstransmitted by the elements 111, 112, 113, 114, 115, 116, 117, 118, and119.

In some implementations, the elements 111, 112, 113, 114, 115, 116, 117,118, and 119 of the transmitting wireless power transfer device 100 andthe elements 151, 152, 153, 154, 155, 156, 157, 158, and 159 may be usedfor in-band communication. For example, the transmitting wireless powertransfer device 100 and the receiving wireless power transfer device 150may communicate using the waveforms generated by their respectiveelements. The transmitting wireless power transfer device 100 andreceiving wireless power transfer device 150 may also communicateout-of-band, for example, using a Bluetooth, Wi-Fi, cellular, or othersuitable wireless connection, or a suitable wired connection.

FIG. 2 shows an example system suitable for beamforming for wirelesspower transfer according to an implementation of the disclosed subjectmatter. The transmitting wireless power transfer device 100 may includetransducers 210, transducer control 220, and a computing device 230,which may include a transducer signal generator 231 and receiverposition detector 235. The transducers 210 may be any suitabletransducers for the transmission of wireless power, such as, forexample, the elements 111, 112, 113, 114, 115, 116, 117, 118, and 119.The transducer control 220 may be any suitable combination of hardwareand software for controlling the transducers 210, for example, based oncontrol signals from the transducer signal generator 231. The computingdevice 230 may be any suitable computing device, such as, for example, acomputer 20 as described in FIG. 18, or component thereof, forimplementing the transducer signal generator 231 and the receiverposition detector 235. The computing device 230 may be a singlecomputing device, or may include multiple connected computing devices,and may be, for example, a laptop, a desktop, an individual server, aserver farm, or a distributed server system, or may be a virtualcomputing device or system. The computing device 230 may be part of acomputing system and network infrastructure, or may be otherwiseconnected to the computing system and network infrastructure. Thetransducer signal generator 231 may be any suitable combination ofhardware and software on the computing device 130 for generating controlsignals that may be used to control the transducers 210. The receiverposition detector 235 may be any suitable combination of hardware andsoftware for detecting the position of a receiving wireless powertransfer device, such as the receiving wireless power transfer device150.

The transducers 210 may be any suitable transducers for the transmissionof wireless power, such as, for example, the elements 111, 112, 113,114, 115, 116, 117, 118, and 119. The transducers 210 may be, forexample, ultrasonic transducers, RF transducers, or optical transducers.The transmitting wireless power transfer device 100 may include anysuitable number of transducers 210, arranged in any suitable manner. Forexample, the transducers 210 may all be arranged in grid pattern on thesame plane, may be arranged across multiple planes at various angles, ormay be arranged on curved or spherical surfaces of the transmittingwireless power transfer device 100. The transducers 210 may operate inreceiving mode or a transmitting mode. In some implementations, thetransducers 210 may operate in both modes at the same time, for example,with certain transducers operating in a receiving mode while othersoperate in a transmitting mode.

The transducer control 220 may be any suitable combination of hardwareand software for controlling the transducers 210, for example, based oncontrol signals from the transducer signal generator 231. The transducercontrol 220 may include any suitable electronics, including generalpurpose or specialized processors and controllers, circuitry, andelectrical connections to connect the computing device 230 to thetransducers 210. The transducer control 220 may also include anysuitable electronics, including general purpose or specializedprocessors and controllers, circuitry, and electrical connections tohandle electrical signals generated by any of the transducers 210operating in a receiving mode. For example, the transducer control 220may include voltage rectifiers and transformers to convert an electricalsignal generated based on received power to a specified current type andvoltage, and to direct the electrical signal to an appropriate form ofenergy storage. The transducer control 220 may also, in conjunction withthe computing device 230, interpret in-band communications received atthe transducers 210. The transducer control 210 may be able to determinethe phase and amplitude of a wave front as experienced at any of thetransducers 210 when operating in a receiving mode. The phasedetermination may be made relative to other transducers 210 which mayreceive the same wave front, and may be made using any suitablemeasurements taken over any suitable period of time at any suitableintervals.

The computing device 230 may be a single computing device, or mayinclude multiple connected computing devices, and may be, for example, alaptop, a desktop, an individual server, a server farm, or a distributedserver system, or may be a virtual computing device or system. Thecomputing device 230 may be part of a computing system and networkinfrastructure, or may be otherwise connected to the computing systemand network infrastructure. The computing device 230 may be part of thesame physical device as the transducers 210, or may be part of aseparate device connected to the transducer 210 through the transducerscontrol 220 through, for example, a wired or wireless connection.

The transducer signal generator 231 may be any suitable combination ofhardware and software on the computing device 130 for generating controlsignals that may be used to control the transducers 210. The transducersignal generator 231 may generate control signals which may be used tocontrol the waveforms generated by the transducers 210. Control signalsgenerated by the transducer signal generator 231 may, for example,indicate the phase, frequency, and amplitude of the waveforms to begenerated by the transducers 210. The transducer signal generator 231may use phases and amplitudes of a received wave front, as determined atthe transducers 210, to generate control signals, for example, using thephase differences as determined at the transducers 210. The transducersignal generator 231 may determine when the transducers 210 enterreceiving and transmitting modes.

The receiver position detector 235 may be any suitable combination ofhardware and software for detecting the position of a receiving wirelesspower transfer device, such as the receiving wireless power transferdevice 150. The position of the receiving wireless power transfer device150, which may be an intended target of wireless power from thetransmitting wireless power transfer device 100, may include thedistance from the transmitting wireless power transfer device 100,angles of a vector between the transmitting wireless power transferdevice 100 and receiving wireless power transfer device 150, and angleof orientation of the receiving wireless power transfer device 150,including the orientation of any transducers, for example, the elements151, 152, 153, 154, 155, 156, 157, 158, and 159, of the receivingwireless power transfer device 100. For example, the receiver positiondetector 235 may receive position data from the receiver wireless powertransfer device 150, including, for example, gyroscope and accelerometerdata. The receiver position detector 235 may use the transducers 210 tolocate the receiving wireless power transfer device 150, for example,transmitting the beam 180, with, for example, a narrow focus, at variousangles until the receiving wireless power transfer device 150 respondsthat it detected the beam 180. The receiver position detector 235 mayalso use any other separate tracking or range-finding devices to locatethe position of the receiving wireless power transfer device 150.

FIG. 3A shows an example arrangement suitable for beamforming forwireless power transfer according to an implementation of the disclosedsubject matter. The receiving wireless power transfer device 150 mayinclude transducers 310, which may include, for example, the elements151, 152, 153, 154, 155, 156, 157, 158, and 159. A transducer signalgenerator 331 of a computing device 330 of the receiving wireless powertransfer device 150 may generate control signals for the generation of acoherent phase beam by the transducers 310. The coherent phase controlsignals may be sent to a transducer control 320, which may control thetransducers 310 to generate a beam 280. The beam 280 may have a coherentphase at its origin across the transducers 310. For example, thewaveforms generated by the elements 151, 152, 153, 154, 155, 156, 157,158, and 159 may all be in phase. The wave front of the beam 280 maypropagate away from the transducers 310. The receiving wireless powertransfer device 150 may transmit the beam 280 for any suitable length oftime. For example, the receiving wireless power transfer device 150 maytransmit the beam 280 for a short duration, to conserve power, or untilan out-of-band confirmation that the beam 280 was detected is receivedfrom the transmitting wireless power transfer device 100. In someimplementations, the beam 280 may be transmitted by the transducers 310using a defined phase pattern. For example, the elements 151, 152, and153 may transmit in phase with each other, the elements 154, 155, and156 may transmit in phase with each other and out-of-phase with theelements 151, 152, and 153 by 45 degrees, and the elements 157, 158, and159 may transmit in phase with each other and out-of-phase with theelements 151, 152, and 153 by 90 degrees.

The transducers 210 may be operating in a receiving mode. For example,the receiving wireless power transfer device 150 may indicate throughout-of-band communications with the transmitting wireless power transferdevice 100 that it intends to transmit the beam 280, or the transducers210 may enter a receiving mode at specified intervals. The transducers210 may detect the beam 280. For example, the wave front of the beam 280may arrive at the elements 111, 112, 113, 114, 115, 116, 117, 118, and119. The transducer control 220 may receive the electrical signalsgenerated by the transducers 210 from the energy carried by the beam280, and may determine properties of the wave front of the beam 280 atthe transducers 210. For example, the transducer control 220 maydetermine the phase and amplitude of the wave front as experienced ateach transducer, or element, of the transducers 210. The determinedproperties of the wave front of the beam 280 as experienced at thetransducers 210 may be sent to the transducer signal generator 231. Insome implementations, the transducer control 220 may pass the electricalsignals as received from the transducers 210 to the transducer signalgenerator 231, which may analyze the electrical signals to determine theproperties of the wave front of the beam 280 as experienced at thetransducers 210.

The phase determinations may be relative to any one of the transducers210. For example, the transducer which first detects the wave front ofthe beam 280 may be considered to have experienced a phase of 0 degreesand the phases of the rest of the transducers 210 may be determinedrelative to this transducer. When the beam 280 is a continuous wave, thephase determined for any transducer may be between 0 and 359 degrees, asa phase of 360 degrees may be equivalent to a phase of 0 degrees. Thephase determination may occur over any suitable number of cycles of thewave front. In some implementations, the beam 280 may be pulsed, whichmay result in full phase differences being detected, starting at 0degrees and with no upper limit, as a 360 degree difference between thephases of two transducers may not indicate that the two transducers arein phase when the beam 280 is pulsed. For example, when the beam 280 ispulsed, two transducers may have a phase difference greater than 360degrees.

FIG. 3B shows an example arrangement suitable for beamforming forwireless power transfer according to an implementation of the disclosedsubject matter. The transducer signal generator 231 of the transmittingwireless power transfer device 100 may generate control signals for thegeneration of a beam by the transducers 210 that may be directed at thereceiving wireless power transfer device 150 based on the phases of thewave front of the beam 280 as experienced by the transducers 210. Forexample, the transducer signal generator 231 generate a control signalthat may cause the transducers 210 to transmit waveforms with the samephase difference experienced by the transducers 210. The phase controlsignals may be sent to the transducer control 220, which may control thetransducers 210 to generate a beam 380. The beam 380 may have a coherentphase across the transducers 310. For example, the waveforms generatedby the elements 111, 112, 113, 114, 115, 116, 117, 118, and 119 may havevarious phases, depending on the phase of the wave front of the beam 280that was experienced by each element. The waveforms from the transducers210 may be phase shifted from the phases experienced by the transducers210 as long as the experienced phase differences are maintained. Thewave front of the beam 380 may be directed towards, and have a coherentphase across, the elements 151, 152, 153, 154, 155, 156, 157, 158, and159, such that each element ideally experiences the wave front with thesame phase as the other elements. The wave front of the beam 380 maypropagate away from the transducers 210 towards the transducers 310.

The transducers 310 may be operating in a receiving mode. For example,the receiving wireless power transfer device 150 may receive anindication through out-of-band communications with the transmittingwireless power transfer device 100 that it intends to transmit the beam380, or the transducers 310 may enter a receiving mode at specifiedintervals, for example, after ceasing transmission of the beam 280. Thetransducers 310 may detect the beam 380. For example, the wave front ofthe beam 380 may arrive at the elements 151, 152, 153, 154, 155, 156,157, 158, and 159. The transducer control 320 may receive the electricalsignals generated by the transducers 310 from the energy carried by thebeam 380, and may supply this energy to an energy storage device 340,which may be, for example, a battery, a capacitor, or any other suitableform of storage for the electrical energy generated by the transducers310. The transducers 310, transducer control 320, and energy storagedevice 340 may include appropriate electronics, circuitry, andconnections to store electrical energy, including, for examplerectifiers and transformers for converting the electrical signals fromthe transducers 310 to a suitable current type and voltage.

FIGS. 4A and 4B show example arrangements suitable for beamforming forwireless power transfer according to an implementation of the disclosedsubject matter. The beam 280 transmitted by the receiving wireless powertransfer device 150 may not be aimed at the transmitting wireless powertransfer device 100. The beam 280 may be the result of the transducers310 transmitting waveforms that are in phase. The direction of the beam280 may depend on the relative locations of the transducers 310 on thereceiving wireless power transfer device 150. For example, if thetransducers 310 are located in a grid on a flat plane, the beam 280 maypropagate outward from the flat plane. As long as the transducers 310are facing the transducers 210, the wave front of the beam 280 mayarrive at the transducers 210, although some part of the wave front maypropagate out into space and miss the transducers 310. The transducers210 may detect variations in phase of the wave front, depending on thepositions of the transducers 210 relative to the positions of thetransducers 310. For example, with the receiving wireless power transferdevice 150 located lower than and to the left of the transmittingwireless power transfer device 100, the wave front of the beam 280 mayfirst arrive at transducers that are located lower on and on the leftside of, when facing towards the transducers, the transmitting wirelesspower transfer device 100. Transducers located higher on, or to theright of, the transmitting wireless power transfer device 100 mayreceive the wave front of the beam 280 later, resulting in a phasedifference in the transducers' experience of the wave front. Phasedifferences may also be introduced due to interference between theconstituent waveforms of the beam 280. When the beam 280 is a continuouswave, the phase difference between the phases experienced by any two ofthe transducers 210 may be no greater than 359 degrees, as twotransducers which experience a phase difference of 360 degrees, or onewavelength, may be in phase. In some implementations, the beam 280 maybe pulsed, which may result in full phase differences being detected, astwo transducers with a phase difference of 360 degrees may not be inphase when the beam 280 is pulsed.

FIG. 5 shows example waveforms suitable for beamforming for wirelesspower transfer according to an implementation of the disclosed subjectmatter. Graph 511 may represent the wave front of the beam 280 asexperienced at a first of the transducers 210. Graph 512 may representthe wave front of the beam 280 as experienced at a second of thetransducers 210. Graph 513 may represent the wave front of the beam 280as experienced at a third of the transducers 210. The beam 280 may becontinuous, or may be pulsed with the graphs 511, 512, and 513representing, for example, the experience of the wave front of a pulseat the transducers. The first of the transducers 210 may be the firsttransducer at which the wave front of the beam 280 arrives, and may beassigned a phase of 0 for the waveform 512. The second of thetransducers 210 may experience the wave front of the beam 280 with aphase difference 520 from the first of the transducers 210, resulting inthe waveform 521. The phase difference 520 may be, for example, 50degrees. The phase difference may be equal to the number of degreesthrough a full wavelength the wave front cycles through at the first ofthe transducers 210 before the wave front arrives at the second of thetransducers 210, or may be a phase difference resulting from, forexample, interference in the wave front after the wave front has arrivedat both the first and second transducers. The interference may be basedon how close to the center or focus of the beam 280 the second of thetransducers 210 is located. The third of the transducers 210 mayexperience the wave front of the beam 280 with a phase difference 530from the first of the transducers 210, resulting in the waveform 513.The phase difference 520 may be, for example, 180 degrees. Whenreceiving the beam 280, any transducer of the transducers 210 may bechosen as the transducer experiencing the wave front of the beam 280with a phase of 0, and the phases experienced by all other transducersmay be determined relative to the chosen transducer.

FIG. 6 shows example waveforms suitable for beamforming for wirelesspower transfer according to an implementation of the disclosed subjectmatter. Graph 611 may represent a waveform for the beam 380 astransmitted at a first of the transducers 210. Graph 612 may represent awaveform for the beam 380 as transmitted at a second of the transducers210. Graph 613 may represent a waveform for the beam 380 as transmittedat a third of the transducers 210. The beam 380 may be continuous, ormay be pulsed with the graphs 611, 612, and 613 representing, forexample, the transmission of the wave front of a pulse from thetransducers. The first of the transducers 210 may transmit a waveform621 that may be same as the waveform 521. The second of the transducers210 may transmit a waveform 622 that may be the same as the waveform522. The waveform 622 may be out-of-phase with the waveform 621 by thesame phase difference that the waveform 522 was out-of-phase with thewaveform 521, for example, the phase difference 520 of 50 degrees. Thethird of the transducers 210 may transmit a waveform 623 that may be thesame as the waveform 523. The waveform 623 may be out-of-phase with thewaveform 621 by the same phase difference that the waveform 523 wasout-of-phase with the waveform 521, for example, the phase difference530 of 180 degrees. The phase differences between the waveforms 521,522, and 523 may be maintained by the waveforms 621, 622, and 623.

FIGS. 7A and 7B show example arrangements suitable for beamforming forwireless power transfer according to an implementation of the disclosedsubject matter. The beam 280 transmitted by the transmitting wirelesspower transfer device 100 may be aimed at the receiving wireless powertransfer device 150. The beam 380 may be the result of the transducers210 transmitting waveforms that maintain the phase difference from eachtransducers' experience of the wave front of the beam 280. The directionof the beam 380 may be the result of interference among the constituentwaveforms of the beam 380, resulting in recreation of the portion of thebeam 280 that arrived at the transducers 210. Destructive interferencedue to the phase differences between the waveforms transmitted by thetransducers 210 may result in the beam 380 being directed towards, andfocusing on, the transducers 310 of the receiving wireless powertransfer device 100. This may reduce the amount of energy carried by thebeam 380 that does not arrive at the transducers 310. The wave front ofthe beam 380 may have across coherent phase at the transducers 310 ofthe receiving wireless power transfer device 150. If the beam 280 wastransmitted using defined phase patterns from the transducers 310, thewave front of the beam 380 may reproduce the defined phase patternacross the transducers 310.

FIG. 8 shows an example arrangement suitable for beamforming forwireless power transfer according to an implementation of the disclosedsubject matter. The transmitting wireless power transfer device 100 maysimulate a beam 880 from the transducers 310 of the receiving wirelesspower transfer device 150. The receiver position detector 235 mayreceive position data, which may indicate the position of the receivingwireless power transfer device absolutely or relative to thetransmitting wireless power transfer device 100. The position data maybe generated in any suitable manner, including, for example, based onaccelerometer data, gyroscopic data, or other positioning data from thereceiving wireless power transfer device 150, any data from any suitabletracking or range finding devices of the transmitting wireless powertransfer device 100, including the transducers 210.

The receiver position data may include the distance and angles betweenthe transmitting wireless power transfer device 100 and the receivingwireless power transfer device 150, as any relative angle of orientationor tilt. The receiver position data may also include locations of thetransducers 310 on the receiving wireless power transfer device 150,include which surfaces of the receiving wireless power transfer device150 various transducers are located on and angles at which varioustransducers may be oriented. The receiver position data may allow thetransducer signal generator 231 to know the location of each of thetransducers 310 relative to each of the transducers 210.

The transducer signal generator 231 may use the receiver position datato simulate a simulated beam 880 originating from the transducers 310.The simulated beam 880 may be simulated as originating with in phasewaveforms transmitted by the transducers 310. The simulated beam 880 mayhave a coherent phase across the transducers 310, and may propagatetowards the transducers 210. The simulation of the propagation of thesimulated beam 880 may include any interface between the constituentsimulated waveforms, and may account for, for example, the type ofwireless power transfer being used and the medium through which thesimulated beam 880 travels, and may attempt to account for losses ofamplitude during propagation. For example, the simulation may accountfor ambient air pressure when the simulated beam 880 is a beam ofultrasonic waves. The simulated beam 880 may be simulated from thetransducers 310 to the transducers 210. The transducer signal generator231 determine that phase and amplitude of the wave front of thesimulated beam 880 that would be experienced at each of the transducers880.

The transducer signal generator 231 may simulate the simulated beam 880in any suitable manner. For example, the transducer signal generator 231may simulate the simulated beam 880 for each of the transducersindividually or as a group, in parallel or in series. For example, thetransducer signal generator 231 may simulate the entire simulated beam880 from the transducers 310 at once, simulating the entire wave frontarriving at the transducers 210, or the transducer signal generator 231may simulate portions of the simulated beam 880, for example, in thechannel between the transducers 310 and individual one of thetransducers 210 or groups of the transducers 210. Portions of thesimulated beam 880 may be simulated in parallel or in series, forexample, depending on the computational resources available to thetransducer signal generator 231. For example, the portion of thesimulated beam 880 between the transducers 210 and the element 111 maybe simulated in parallel with a portion other simulated beam 880 betweenthe transducers 210 and the element 112. The simulated beam 880 may besimulated with any suitable granularity. For example, the simulated beam880 may be simulated at intervals of 1/100000 of a second. The simulatedbeam 880 may also be simulated using a calculation or approximation,which may determine the properties of the simulated beam 880 at thetransducers 210 directly from the properties of the simulated beam atthe transducers 310 without simulating the simulated beam 880 in routebetween the transducers 310 and the transducers 210.

The transducer signal generator 231 may generate control signals for thegeneration of a beam by the transducers 210 that may be directed at thereceiving wireless power transfer device 150 based on the phases of thewave front of the simulated beam 880 as experienced, in simulation, bythe transducers 210. For example, the transducer signal generator 231generate a control signal that may cause each transducer to transmitwith the same phase that was experienced by that transducer. The phasecontrol signals may be sent to the transducer control 220, which maycontrol the transducers 210 to generate a beam, such as the beam 380.The beam 380 may have a coherent phase across the transducers 310. Forexample, the waveforms generated by the elements 111, 112, 113, 114,115, 116, 117, 118, and 119 may have various phases, depending on thephase of the wave front of the simulated beam 880 that was experienced,in simulation, by each element. The wave front of the beam 380 may bedirected towards, and have a coherent phase across, the elements 151,152, 153, 154, 155, 156, 157, 158, and 159, such that each elementideally experiences the wave front with the same phase as the otherelements. The wave front of the beam 380 may propagate away from thetransducers 210 towards the transducers 310.

The simulation of the simulated beam 880 may be performed at anysuitable time or interval. For example, the transmitting wireless powertransfer device 100 may simulate the simulated beam 880 aftercommunicating in-band or out-of-band with the receiving wireless powertransfer device 150. For example, the receiving wireless power transferdevice 150 may indicate that it wishes to be a target for wirelesspower. The simulation of the beam 880 may be performed at any interval,including, for example, on a regular update cycle, for example, toaccount for a change in the relative positions of the transmittingwireless power transfer device 100 and the receiving wireless powertransfer device 150 or to update a previously performed simulation thatdid not simulate the simulated beam 880 at all of the transducers 210 orfrom all of the transducers 310. Simulation using calculation orapproximation of the properties of the simulated beam 880 at thetransducers 210 may allow for faster generation of control signals forthe transducers 210 and faster changing of the properties of the beam380, for example, to keep up with changes in the relative positions ofthe transmitting wireless power transfer device 100 and the receivingwireless power transfer device 150. For example, as the receivingwireless power transfer device 150 moves, the simulated beam 880 may berapidly and continuously simulated using calculation or approximation sothat the new control signals may be quickly generated based on the newposition of the receiving wireless power transfer device 150 and thetransducers 210 may transmit the beam 380 using the phases in the newcontrol signals before they are too far out of date due to furthermovement of the receiving wireless power transfer device 150. The numberof transducers 210 used by the transmitting wireless power transferdevice 100 may be adjusted, for example, as the simulation of the wavefront for additional transducers may increase the overall efficiency ofthe transfer of wireless power, allowing for fewer transducers to beused to transmit the wireless power.

FIG. 9 shows an example arrangement suitable for beamforming forwireless power transfer according to an implementation of the disclosedsubject matter. The simulated beam 880 may be simulated in portions. Forexample, the channel 910 may be a portion of the simulated beam 880between the transducers 310 of the receiving wireless power transferdevice 150, for example, the elements 151, 152, 153, 154, 155, 156, 157,158, and 159, and one of the transducers 210, for example, the element113. The channel 910 may be simulated based on the portions of thesimulated waveforms originating at the elements 151, 152, 153, 154, 155,156, 157, 158, and 159 that account for the wave front of the simulatedbeam 880 at the element 113. The phase and amplitude of the wave frontof the wave front of the simulated beam 880 at the element 113 may bedetermined based on the simulation of the simulated waveforms in thechannel 910. Similarly, additional channels between the elements 151,152, 153, 154, 155, 156, 157, 158, and 159 and each of the channels 111,112, 114, 115, 116, 117, 118 and 119 may also be simulated, in parallelor in series with the simulation of the channel 910.

FIG. 10 shows an example arrangement suitable for beamforming forwireless power transfer according to an implementation of the disclosedsubject matter. The simulated beam 880 may be simulated as originatingfrom points on the receiving wireless power transfer device 150 that notbe located on the transducers 310. For example, the channel 1010 may besimulated based on waveforms originating from points on the surface ofthe receiving wireless power transfer device 150 among the elements 151,152, 153, 154, 155, 156, 157, 158, and 159. Points of origination otherthan the transducers 310 may be used to reduce the amount computationrequired to simulate the simulated 880. For example, instead ofsimulating the waveforms of the simulated beam 880 in the channel 1010from each of the elements 151, 152, 153, 154, 155, 156, 157, 158, and159, the channel 1010 may be simulated from six points, with each pointin between two adjacent elements on the same row. The phase andamplitude experienced, in simulation, by the element 113 based on thewave front of the portion of the simulated beam 880 in the channel 1010as simulated based on six points may be approximations of the phase andamplitude the element 113 would experience in simulation if waveformswere simulated from each of the elements 151, 152, 153, 154, 155, 156,157, 158, and 159.

FIG. 11 shows an example procedure suitable for beamforming for wirelesspower transfer according to an implementation of the disclosed subjectmatter. At 1100, a wave front of a beam generated with coherent phasemay be received. For example, the transducers 210 of the transmittingwireless power transfer device 100 may receive the wave front of thebeam 280. The beam 280 may have been generated by the transducers 310 ofthe of the receiving wireless power transfer device 150. The transducers310 may generate waveforms in phase, so that the beam 280 may have acoherent phase at its origin. In some implementations, the beam 280 maybe generated from waveforms with defined phase patterns.

At 1102, the phases of the wave front may be determined at thetransducers. For example, the phases of the wave front of the beam 280may be determined as experienced at the transducers 210, for example, byany suitable combination of the transducer control 220 and thetransducer signal generator 231. The phases may be determined in anysuitable manner, using any suitable measurements of any suitable lengthof time made at any suitable intervals. The amplitude of the wave frontof the beam 280 as experienced at the transducers 210 may also bedetermined. Phase determination may be made for all of the transducers210, or some subset of the transducers 210, for example, depending onthe locations of the transducers 210, as some of the transducers 210 maynot receive any part of the wave front of the beam 280.

At 1104, control signals based on the determined phases may begenerated. For example, the transducer signal generator 231 may generatecontrol signals which may be used to cause the transducers 210 totransmit waveforms based on the determined phases for each of thetransducers 210. The control signals may be any suitable signals thatmay be used by, for example, the transducer controller 220 to controlthe transducers 210.

At 1106, waveforms may be transmitted from the transducers based on thetransducer control signals. For example, the transducer controller 220may provide the control signals from the transducer signal generator 231to the transducers 210. This may cause the transducers 210 to transmitwaveforms in accordance with the control signals, for example, with thephases and amplitudes specified in the control signals. The waveformsfrom the transducers 210 may constitute the beam 380, which may bedirected at and focused on the transducers 310, and may have a wavefront with a coherent phase across the transducers 310.

FIG. 12 shows an example procedure suitable for beamforming for wirelesspower transfer according to an implementation of the disclosed subjectmatter. At 1200, the position of a receiving device may be determined.For example, the receiver position detector 235 of the transmittingwireless power transfer device 100 may receive position data indicatingthe position of the receiving wireless power transfer device 150. Thereceiver position data may include, for example, distance and anglesbetween the transmitting wireless power transfer device 100 andreceiving wireless power transfer device 150, the orientation of thereceiving wireless power transfer device 150, and the location andorientation of the transducers 310.

At 1202, waveforms generated with a coherent phase at the receivingdevice may be simulated. For example, the transmitting wireless powertransfer device 100 may simulate, using the transducer signal generator231 and any available computing devices, waveforms generated by thetransducers 310 that are in phase. The simulated waveforms may besimulated as originating from the positions of the transducers 310 onthe receiving wireless power transfer device 150, or from other selectedpoints on the receiving wireless power transfer device 150, asdetermined by the receiver position detector 235. The simulatedwaveforms may constitute the simulated beam 880. The simulated beam 880may be simulated in its entirety, or may be simulated in portions, forexample, based on channels between the transducers 310 and each of thetransducers 210.

At 1204, the phases of the simulated wave front may be determined at thetransducer location. For example, the phases of the wave front of thesimulated beam 880 may be determined as they would be experienced at thelocations of the transducers 210, for example, by the transducer signalgenerator 231. The phases may be determined in any suitable manner,using any suitable measurements of the simulated beam 880 of anysuitable length of time made at any suitable intervals. The amplitude ofthe wave front of the simulated beam 880 as it would be experienced atthe transducers 210 may also be determined. Phase determination may bemade for all of the transducers 210, or some subset of the transducers210, for example, depending on computational resources available and thelocations of the transducers 210, as some of the transducers 210 may notreceive any part of the wave front of the simulated beam 880.

At 1206, control signals based on the determined phases may begenerated. For example, the transducer signal generator 231 may generatecontrol signals which may be used to cause the transducers 210 totransmit waveforms based on the determined phases for each of thetransducers 210. The control signals may be any suitable signals thatmay be used by, for example, the transducer controller 220 to controlthe transducers 210.

At 1208, waveforms may be transmitted from the transducers based on thetransducer control signals. For example, the transducer controller 220may provide the control signals from the transducer signal generator 231to the transducers 210. This may cause the transducers 210 to transmitwaveforms in accordance with the control signals, for example, with thephases and amplitudes specified in the control signals. The waveformsfrom the transducers 210 may constitute the beam 380, which may bedirected at and focused on the transducers 310, and may have a wavefront with a coherent phase across the transducers 310.

FIG. 13 shows an example system suitable for beamforming for wirelesspower transfer according to an implementation of the disclosed subjectmatter. A notional field r_(xE) 1360 may be emitted from a receivingwireless power transfer device 150. The notional field notional fieldr_(xE) 1360 may be a notional wave front, and may not be physicallyemitted from the elements 151, 152, 153, 154, 155, 156, 157, 158, and159. The notional field r_(xE) 1360 may be represented by aphase/amplitude map r_(xE)(x, y), and may have a linear phase profile ina plane P₂ 1340, which may be a plane of an aperture 1350 of thereceiving wireless power transfer device 150. The aperture 1350 may be,for example, an area of the receiving wireless power transfer device 150including elements, such as the elements 151, 152, 153, 154, 155, 156,157, 158, and 159, which may serve as the source of the notional fieldr_(xE) 1360. The plane P₂ 1340 may be a plane on which the aperture 1350is located.

A Fourier transform in the plane P₂ 1340 of the phase/amplitude mapr_(xE)(x, y) for the notional field r_(xE) 1360 may be determined,resulting in a spatial frequency representation in the plane P₂ 1340. AFourier transform may be used to determine R_(xE)(v_(x), v_(y)), whichmay be the Fourier transform of the phase/amplitude map r_(xE)(x, y),and may be the spatial frequency representation in the plane P₂ 1340 ofthe notional field r_(xE) 1360, that would be emitted from the aperture1350 of the receiving wireless power transfer device 150 based on thephase/amplitude map r_(xE)(x, y).

The notional field r_(xE), with the phase/amplitude map r_(xE)(x, y),may be propagated from the plane P₂ 1340 of the aperture 1350 of thereceiving wireless power transfer device 150 to plane P₁ 1320 of anaperture 1310 of the transmitting wireless power transfer device 100 inthe spatial frequency domain. This may produce a notional field t_(xR)1330 in the plane P₁ 1320. The phase/amplitude map of t_(xR)(x, y) maydescribe the phase and amplitudes of the notional wave front that wouldbe received at the aperture 1310 of the transmitting wireless powertransfer device 100 based on the notional field r_(xE) 1360 with thephase/amplitude map r_(xE)(x, y) being notionally emitted from theaperture 1350 of the receiving wireless power transfer device 150.t_(xR)(x, y) may be determined according to T_(xR)(v_(x),v_(y))=R_(xE)(v_(x), v_(y))H(v_(x), v_(y)), where T_(xR)(v_(x), v_(y))is the Fourier Transform of t_(xR)(x, y), and where H(v_(x),v_(y))=e^(jk) ^(z) ^(d) where j=√{square root over (−1)},

${k_{z} = {2\pi \sqrt{\frac{1}{\lambda^{2\;}} - v_{x} - v_{y}}}},$

λ is the wavelength of the plane wave associated with the vector {rightarrow over (k)}, which may be normal to the plane wave, and d is thedisplacement on the z-axis between the plane P₂ 1340 and the plane P₁1320, where {right arrow over (k)}(v_(x), v_(y))=

k_(x), k_(y), k_(z)

, with v_(x) and v_(y) being transverse spatial frequencies in theplane. Additionally, k_(x)=2πv_(x) and k_(y)=2πv_(y). The magnitude ofthe plane wave associated with the vector

$\overset{\rightarrow}{k} = {k = {\frac{2\pi}{\lambda}.}}$

The Fourier transform may be performed by, for example, the transmittingwireless power transfer device 100. For example, the receiver positiondetector 235 may receive receiver position data from the receivingwireless power transfer device 150. The transducer signal generator 220may use the receiver position data to determine the location of thenotional field r_(xE) 1360 relative to the aperture 1310 in the plane P₁1320. The transducer signal generator 220 may determine any phasecorrections that may be applied if the plane P₂ 1340 is not parallel tothe plane P₁ 1320 as indicated by the receiver position data. Thetransducer signal generator 220 may then apply a Fourier transform tothe phase/amplitude map r_(xE)(x, y) to determine R_(xE)(v_(x), v_(y)),which may be the spatial frequency representation of r_(xE)(x, y) in theaperture 1350. The transducer signal generator 220 may then apply thetransformation kernel H(v_(x), v_(y)) to R_(xE)(v_(x), v_(y)) todetermine the propagation of the notional field r_(xE) 1360 through freespace to the plane P₁ 1320 and the aperture 1310, resulting in thespatial frequency representation T_(xR)(v_(x), v_(y)) in the aperture1310. The transducer signal generator 220 may then apply an inverseFourier transform to T_(xR)(v_(x), v_(y)). The result may be thenotional field t_(xR) 1330 and its corresponding phase/amplitude mapt_(xR)(x, y) at the aperture 1310.

FIG. 14 shows an example system suitable for beamforming for wirelesspower transfer according to an implementation of the disclosed subjectmatter. The phase/amplitude map t_(xR)(x, y) may be windowed to theaperture 1310 of the transmitting wireless power transfer device 100 anda phase conjugate may be applied to the complex amplitude/phase signalto determine the phase/amplitude map that may reconstruct the notionalfield r_(xE) 1360 represented by the phase/amplitude map r_(xE)(x, y) atthe aperture 1350 of the receiving wireless power transfer device 150.Resampling of the phase/amplitude map t_(xR)(x, y) may be necessary ifthe pitch of the constructed plane P₂ 1340 of the aperture 1350 of thereceiving wireless power transfer device 150 does not correspond to theelement pitch of the transmitting wireless power transfer device 100.

For example, t_(xE)(x, y) may be the phase/amplitude map of the physicalfield t_(xE) 1410 emitted by elements of the transmitting wireless powertransfer device 100, for example, as an ultrasonic beam, intended toproduce the desired complex field in the P₂ 1340 of the aperture 1350 ofthe receiving wireless power transfer device 150. The phase/amplitudemap t_(xE)(x, y) may map the physical field t_(xE) 1410 at the elementsof the transmitting wireless power transfer device 100. t_(xE)(x, y) maybe determined in the spatial domain according to t_(xE)(x, y)=t_(xR)*(x,y)A_(tx)(x, y) where t_(xR)*(x, y) is the complex conjugate of t_(xR)(x,y), and A_(tx)(x, y) is the aperture 1310 of the transmitting wirelesspower transfer device 100, as only the portion of t_(xR)(x, y) whichoverlaps the aperture 1310 of the transmitting wireless power transferdevice 100 may be physically phase-conjugated and re-radiated by theelements of the transmitting wireless power transfer device 100.

The magnitude of the phase/amplitude map t_(xE)(x, y) may be normalizedto optimize the desired power level transmitted from the transmittingwireless power transfer device 100. This may include maximizing thepower transmitted by the transmitting wireless power transfer device100, tuning to a particular desired power level, for example, asindicated by the receiving wireless power transfer device, 150 anddividing the total available power of the transmitting wireless powertransfer device 100 over multiple receiving wireless power transferdevices 150. Apertures may be combined through linear superposition.Normalization and prediction of power delivered may be determined priorto or after the combination of apertures depending upon the resultdesired.

r_(xR)(x, y) may be the phase/amplitude map of the physical field r_(xR)1420 received in the plane P₂ 1340 of the aperture 1350 of the receivingwireless power transfer device 150, for example, as the wave front of anultrasonic beam from the elements of the transmitting wireless powertransfer device 100. When the transmitting wireless power transferdevices 100 emits a physical field, such as the ultrasonic beam, basedon the phase/amplitude map t_(xE)(x, y), the phase/amplitude mapr_(xR)(x, y) may be predicted by R_(xR)(v_(x), v_(y))=T_(xE)(v_(x),v_(y))H(v_(x), v_(y)) where T_(xE)(v_(x), v_(y)) is the Fouriertransform of t_(xE)(x, y) and R_(xR)(v_(x), v_(y)) is the Fouriertransform of r_(xR)(x, y).

For example, the transducer signal generator 231 may generate phasecontrol signals which may be sent to the transducer control 220. Thephase control signals may then be used to control the transducers 210,resulting in the transducers 210 outputting the physical field t_(xE)1410, which may be an ultrasonic beam such as the beam 380, with thephase/amplitude map of t_(xE)(x, y) at the location of the transducers210. This may result in the production of the physical field r_(xR) 1420at the transducers 310 of the receiving wireless power transfer device100, for example, in the form of a wave front of the beam 380. Thephase/amplitude map at the transducers 310 may be, for example,r_(xR)(x, y), and may have coherent phase and uniform amplitude.

FIG. 15 shows an example system suitable for beamforming for wirelesspower transfer according to an implementation of the disclosed subjectmatter. A transformation kernel 1510 may be used to determine thenotional field the notional field t_(xR) 1330 from the notional fieldnotional field r_(xE) 1360. The transformation kernel 1510 may be, forexample, H(v_(x), v_(y)) and may be a spatial-frequency domain transferfunction that may define the Fourier transform of the point spreadfunction for Fraunhofer diffraction at the orthonormal distance betweenthe aperture 1320 of the transmitting wireless power transfer device 100and the center point of the aperture 1350 of the receiving wirelesspower transfer device 150.

FIG. 16 shows an example arrangement suitable for beamforming forwireless power transfer according to an implementation of the disclosedsubject matter. The plane P₂ 1340 of the aperture 1350 of the receivingwireless power transfer device 150 may not be parallel to the plane P₁1320, for example, due to the receiving wireless power transfer device150 being oriented at angle to the transmitting wireless power transferdevice 100, or due to the arrangement of elements on the receivingwireless power transfer device 150 and/or the transmitting wirelesspower transfer device 100. Phase corrections may be determined that maybe applied to each element of the aperture 1350 of the receivingwireless power transfer device 150 to make the aperture 1350 of thereceiving wireless power transfer device 150 quasi-parallel to the planeP₁ 1320 of the aperture 1310 of the transmitting wireless power transferdevice 100. For example, a first-order approximation may be made thatthe apparent width of the aperture 1310 of the transmitting wirelesspower transfer device 100 remains constant from the perspective of theplane P₂ 1340 of the aperture 1350 of the receiving wireless powertransfer device 150, for example, as a square aperture driven with equalamplitude across its face. If the receiving wireless power transferdevice 150 has a flat phase profile across its surface then theresulting phase profile, as part of a phase/amplitude map, in theparallel plane, for example, the plane P₁ 1320 of the aperture 1310 ofthe transmitting wireless power transfer device 100, may be calculatedby normalizing the receiving wireless power transfer device's actualsurface normal unit vector {right arrow over (n_(r))} to length

${\overset{\rightarrow}{k}} = \frac{2\pi}{\lambda}$

and taking it to be the central {right arrow over (k)} of the emittedangular spectrum from the aperture 1350 of the receiving wireless powertransfer device 100, λ is the wavelength of the plane wave associatedwith the vector {right arrow over (k)}, which may be normal to the planewave. The phase profile of the phase/amplitude map r_(xE)(x, y) at theplane P₂ 1350 may be approximately given by ϕ_(r)(x, y)=e^(−i(k) ^(rx)^(x+k) ^(ry) ^(y)) where {right arrow over (k_(r))}=

k_(rx), k_(ry), k_(rz)

=|{right arrow over (k)}|·{right arrow over (n_(r))}.

This may be a rotation of a true flat phase profile of the aperture 1350of the receiving wireless power transfer device 150 to give the notionalfield r_(xE) 1360, or wave front, represented by the phase/amplitude mapr_(xE)(x, y), a linear phase profile in the plane P₂ 1340 bymultiplication by a complex exponential. This may be a shift of theangular spectrum in spatial frequency to be centered around (v_(rx),v_(ry))=(k_(rx), k_(ry))/2π. Similarly, after r_(xR)(x, y), which may bethe phase/amplitude map for the physical field r_(xR) 1420, or wavefront, received at the elements of the aperture 1340 of the receivingwireless power transfer device 150 is calculated in the plane P₂ 1340 itmay be rotated back into the plane P₂ 1340 of the aperture 1340 of thereceiving wireless power transfer device 150 by division by the samecomplex exponential.

FIG. 17 shows an example process suitable for beamforming for wirelesspower transfer according to an implementation of the disclosed subjectmatter. At 1700, the position of a receiving device may be determined.For example, the receiver position detector 235 of the transmittingwireless power transfer device 100 may receive position data indicatingthe position of the receiving wireless power transfer device 150. Thereceiver position data may include, for example, distance and anglesbetween the transmitting wireless power transfer device 100 andreceiving wireless power transfer device 150, the orientation of thereceiving wireless power transfer device 150, and the location andorientation of the transducers 310.

At 1702, a notional field in the plane of the receiving device may bedetermined. For example, the transmitting wireless power transfer device100 may determine, using the transducer signal generator 231 and anyavailable computing devices, a representation of the notional fieldr_(xE) 1360 in the plane P₂ 1340 of the aperture 1350. The notionalfield notional field r_(xE) may be represented as originating from thepositions of the transducers 310 on the receiving wireless powertransfer device 150, or from other selected points on the receivingwireless power transfer device 150, as determined by the receiverposition detector 235. The representation may be, for example, thephase/amplitude map r_(xE)(x, y), which may represent the phase andamplitude of the notional field r_(xE) 1360 at the location of thetransducer 310, for example, in the aperture 1350.

At 1704, the notional field in the plane of the receiving device may beprojected to the plane of the transmitting device. For example, thetransducer signal generator 231 may determine the phase/amplitude mapt_(xR)(x, y) of the notional field notional field t_(xR) 1330 in theplane P₁ 1320 of the aperture 1310, for example, at the transducers 210,based on the propagation of the notional field r_(xE) 1360 from theplane P₂ 1340 to the plane P₁ 1320. The propagation may be determinedby, for example, use of Fourier transforms. For example, the transducersignal generator 231 may determine R_(xE)(v_(x), v_(y)), which may bethe Fourier transform of the phase/amplitude map r_(xE)(x, y), and maybe the spatial frequency representation in the plane P₂ 1340 of thenotional field r_(xE) 1360. t_(xR)(x, y) may be determined according toT_(xR)(v_(x), v_(y))=R_(xE)(v_(x), v_(y))H(v_(x), v_(y)), whereT_(xR)(v_(x), v_(y)) is the Fourier Transform of t_(xR)(x, y), and whereH(v_(x), v_(y))=e^(jk) ^(z) ^(d) where

${j = \sqrt{- 1}},{k_{z} = {2\pi \sqrt{\frac{1}{\lambda^{2}} - v_{x} - v_{y}}}},$

λ is the wavelength of the plane wave associated with the vector {rightarrow over (k)}, which may be normal to the plane wave, and d is thedisplacement on the z-axis between the plane P₂ 1340 and the plane P₁1320. {right arrow over (k)}(v_(x), v_(y))=

k_(x), k_(y), k_(z)

, with v_(x) and v_(y) being transverse spatial frequencies in theplane. k_(x)=2πv_(x) and k_(y)=2πv_(y). The magnitude of the plane waveassociated with the vector

$\overset{\rightarrow}{k} = {k = {\frac{2\pi}{\lambda}.}}$

At 1706, control signals based on the notional field in the plane of thetransmitting device may be generated. For example, the transducer signalgenerator 231 may generate control signals which may be used to causethe transducers 210 to transmit waveforms based on the phase/amplitudemap t_(xR)(x, y) for the notional field t_(xR) 1330. The control signalsmay be based on the phase/amplitude map t_(xE)(x, y) which may map thephysical field t_(xE) 1410. The phase/amplitude map t_(xR)(x, y) may bewindowed to the aperture 1310 of the transmitting wireless powertransfer device 100 and a phase conjugate may be applied to the complexamplitude/phase signal according to t_(xE)(x, y)=t_(xR)*(x, y)A_(tx)(x,y) where t_(xR)*(x, y) is the complex conjugate of t_(xR)(x, y), andA_(tx)(x, y) is the aperture 1310 of the transmitting wireless powertransfer device 100. Resampling of the phase/amplitude map t_(xR)(x, y)may be necessary if the pitch of the constructed plane P₂ 1340 of theaperture 1350 of the receiving wireless power transfer device 150 doesnot correspond to the element pitch of the transmitting wireless powertransfer device 100. The control signals may be any suitable signalsthat may be used by, for example, the transducer controller 220 tocontrol the transducers 210.

At 1708, waveforms may be transmitted from the transducers based on thetransducer control signals. For example, the transducer controller 220may provide the control signals from the transducer signal generator 231to the transducers 210. This may cause the transducers 210 to transmitwaveforms in accordance with the control signals, for example, with thephases and amplitudes specified in the control signals. The waveformsfrom the transducers 210 may constitute the beam 380, which may bedirected at and focused on the transducers 310, and may have a wavefront with a coherent phase across the transducers 310.

Embodiments of the presently disclosed subject matter may be implementedin and used with a variety of component and network architectures. FIG.18 is an example computer system 20 suitable for implementingembodiments of the presently disclosed subject matter. The computer 20includes a bus 21 which interconnects major components of the computer20, such as one or more processors 24, memory 27 such as RAM, ROM, flashRAM, or the like, an input/output controller 28, and fixed storage 23such as a hard drive, flash storage, SAN device, or the like. It will beunderstood that other components may or may not be included, such as auser display such as a display screen via a display adapter, user inputinterfaces such as controllers and associated user input devices such asa keyboard, mouse, touchscreen, or the like, and other components knownin the art to use in or in conjunction with general-purpose computingsystems.

The bus 21 allows data communication between the central processor 24and the memory 27. The RAM is generally the main memory into which theoperating system and application programs are loaded. The ROM or flashmemory can contain, among other code, the Basic Input-Output system(BIOS) which controls basic hardware operation such as the interactionwith peripheral components. Applications resident with the computer 20are generally stored on and accessed via a computer readable medium,such as the fixed storage 23 and/or the memory 27, an optical drive,external storage mechanism, or the like.

Each component shown may be integral with the computer 20 or may beseparate and accessed through other interfaces. Other interfaces, suchas a network interface 29, may provide a connection to remote systemsand devices via a telephone link, wired or wireless local- or wide-areanetwork connection, proprietary network connections, or the like. Forexample, the network interface 29 may allow the computer to communicatewith other computers via one or more local, wide-area, or othernetworks, as shown in FIG. 19.

Many other devices or components (not shown) may be connected in asimilar manner, such as document scanners, digital cameras, auxiliary,supplemental, or backup systems, or the like. Conversely, all of thecomponents shown in FIG. 18 need not be present to practice the presentdisclosure. The components can be interconnected in different ways fromthat shown. The operation of a computer such as that shown in FIG. 18 isreadily known in the art and is not discussed in detail in thisapplication. Code to implement the present disclosure can be stored incomputer-readable storage media such as one or more of the memory 27,fixed storage 23, remote storage locations, or any other storagemechanism known in the art.

FIG. 19 shows an example arrangement according to an embodiment of thedisclosed subject matter. One or more clients 10, 11, such as localcomputers, smart phones, tablet computing devices, remote services, andthe like may connect to other devices via one or more networks 7. Thenetwork may be a local network, wide-area network, the Internet, or anyother suitable communication network or networks, and may be implementedon any suitable platform including wired and/or wireless networks. Theclients 10, 11 may communicate with one or more computer systems, suchas processing units 14, databases 15, and user interface systems 13. Insome cases, clients 10, 11 may communicate with a user interface system13, which may provide access to one or more other systems such as adatabase 15, a processing unit 14, or the like. For example, the userinterface 13 may be a user-accessible web page that provides data fromone or more other computer systems. The user interface 13 may providedifferent interfaces to different clients, such as where ahuman-readable web page is provided to web browser clients 10, and acomputer-readable API or other interface is provided to remote serviceclients 11. The user interface 13, database 15, and processing units 14may be part of an integral system, or may include multiple computersystems communicating via a private network, the Internet, or any othersuitable network. Processing units 14 may be, for example, part of adistributed system such as a cloud-based computing system, searchengine, content delivery system, or the like, which may also include orcommunicate with a database 15 and/or user interface 13. In somearrangements, an analysis system 5 may provide back-end processing, suchas where stored or acquired data is pre-processed by the analysis system5 before delivery to the processing unit 14, database 15, and/or userinterface 13. For example, a machine learning system 5 may providevarious prediction models, data analysis, or the like to one or moreother systems 13, 14, 15.

The foregoing description, for purpose of explanation, has beendescribed with reference to specific embodiments. However, theillustrative discussions above are not intended to be exhaustive or tolimit embodiments of the disclosed subject matter to the precise formsdisclosed. Many modifications and variations are possible in view of theabove teachings. The embodiments were chosen and described in order toexplain the principles of embodiments of the disclosed subject matterand their practical applications, to thereby enable others skilled inthe art to utilize those embodiments as well as various embodiments withvarious modifications as may be suited to the particular usecontemplated.

1. (canceled)
 2. A method comprising: generating a spatial frequencyrepresentation of a notional field in a plane of an aperture of a firstwireless power transfer device; determining a phase/amplitude map for asecond notional field in a plane of an aperture of a second wirelesspower transfer device based on the spatial frequency representation ofthe notional field in the plane of the aperture of the first wirelesspower transfer device and a position of the first wireless powertransfer device relative to the second wireless power transfer device;and generating control signals for one or more transducer elements ofthe second wireless power transfer device based on the determinedphase/amplitude map for the second notional field in the plane of theaperture of the second wireless power transfer device.
 3. The method ofclaim 2, wherein generating a spatial frequency representation of thenotional field in the plane of the aperture of the first wireless powertransfer device further comprises performing a Fourier transform on aphase/amplitude map for the notional field in the plane of the apertureof the first wireless power transfer device.
 4. The method of claim 2,further comprising: supplying the control signals for the one or moretransducer elements to the one or more transducer elements; andtransmitting waveforms from the one or more transducer elements based onthe supplied control signals.
 5. The method of claim 2, whereindetermining a phase/amplitude map for a second notional field in a planeof an aperture of the second wireless power transfer device based on thespatial frequency representation of the notional field in the plane ofthe aperture of the second wireless power transfer device and theposition of the first wireless power transfer device further comprises:determining a spatial frequency representation of the second notionalfield based on a propagation of the notional field from the plane of theaperture of the first wireless power transfer device to the plane of theaperture of the second wireless power transfer device; and performing aninverse Fourier transform on the spatial frequency representation of thesecond notional field to determine the phase/amplitude map of the secondnotional field.
 6. The method of claim 2, wherein determining a spatialfrequency representation of the phase/amplitude map of the secondnotional field based on a propagation of the notional field from theplane of the aperture of the first wireless power transfer device to theplane of the aperture of the second wireless power transfer devicefurther comprises: applying a transformation kernel to the spatialfrequency representation of the notional field in the plane of theaperture of the first wireless power transfer device to determine thespatial frequency representation of the second notional field in theplane of the aperture of the second wireless power transfer device. 7.The method of claim 2, wherein generating control signals for one ormore transducer elements of the second wireless power transfer devicebased on the determined phase/amplitude map for the second notionalfield in the plane of the aperture of the second wireless power transferdevice further comprises: windowing the complex conjugate of thedetermined phase/amplitude map for the second notional field in theplane of the aperture of the second wireless power transfer device tothe aperture of the second wireless power transfer device.
 8. The methodof claim 2, further comprising determining phase corrections for theaperture of the first wireless power transfer device that make thephase/amplitude map of the notional field quasi-parallel to the plane ofthe aperture of the second wireless power transfer device.
 9. The methodof claim 2, wherein the phase/amplitude map of the notional fieldcomprises coherent phase.
 10. A system for beamforming for wirelesspower transfer comprising: a plurality of elements adapted andconfigured to transmit waveforms for a transmitted beam based onsupplied control signals; a receiver position detector adapted todetermine a position of a receiving wireless power transfer device; anda computing device comprising a transducer signal generator configuredto generate a spatial frequency representation of a notional field in aplane of an aperture of a receiving wireless power transfer device,determine a phase/amplitude map for a second notional field in a planeof an aperture of a transmitting wireless power transfer devicecomprising the plurality of elements based on the spatial frequencyrepresentation of the notional field in the plane of the aperture of thereceiving wireless power transfer device and the position of thereceiving wireless power transfer device, and generate control signalsfor one or more of the plurality of elements based on the determinedphase/amplitude map for the second notional field in the plane of theaperture of the transmitting wireless power transfer device.
 11. Thesystem of claim 10, wherein the transducer signal generator generatesthe spatial frequency representation of the notional field in the planeof the aperture of the receiving wireless power transfer device byperforming a Fourier transform on a phase/amplitude map for the notionalfield in the plane of the aperture of the receiving wireless powertransfer device
 12. The system of claim 10, wherein the transducersignal generator is further configured to supply the control signals forone or more of the plurality of elements to the one or more of theplurality of elements.
 13. The system of claim 12, further comprising atransducer control adapted and configured to receive the control signalsfrom the transducer signal generator and supply the control signals tothe one or more of the plurality of elements.
 14. The system of claim10, wherein the aperture of the receiving wireless power transfer deviceis located at one or more transducer elements of the receiving wirelesspower transfer device.
 15. The system of claim 11, wherein thephase/amplitude map represents the notional field in the plane of theaperture of the receiving wireless power transfer device at the one ormore transducer elements of the receiving wireless power transferdevice.
 16. The system of claim 11, wherein the transducer signalgenerator is configured to determine the phase/amplitude map for thesecond notional field in a plane of the aperture of the transmittingwireless power transfer device based on the spatial frequencyrepresentation of the notional field in the plane of the aperture of thereceiving wireless power transfer device and the position of thereceiving wireless power transfer device by determining a spatialfrequency representation of the second notional field based on apropagation of the notional field from the plane of the aperture of thereceiving wireless power transfer device to the plane of the aperture ofthe transmitting wireless power transfer device, and performing aninverse Fourier transform on the spatial frequency representation of thesecond notional field to determine the phase/amplitude map of the secondnotional field.
 17. The system of claim 16, wherein the wherein thetransducer signal generator is configured to determine the spatialfrequency representation of the phase/amplitude map of the secondnotional field based on the propagation of the notional field from theplane of the aperture of the receiving wireless power transfer device tothe plane of the aperture of the transmitting wireless power transferdevice by applying a transformation kernel to the spatial frequencyrepresentation of the notional field in the plane of the aperture of thereceiving wireless power transfer device to determine the spatialfrequency representation of the second notional field in the plane ofthe aperture of the transmitting wireless power transfer device.
 18. Thesystem of claim 10, wherein the transducer signal generator isconfigured to generate control signals for the one or more of theplurality of transducer elements of the transmitting wireless powertransfer device based on the determined phase/amplitude map for thesecond notional field in the plane of the aperture of the transmittingwireless power transfer device by windowing the complex conjugate of thedetermined phase/amplitude map for the second notional field in theplane of the aperture of the transmitting wireless power transfer deviceto the aperture of the transmitting wireless power transfer device. 19.The system of claim 10, further comprising determining phase correctionsfor the aperture of the receiving wireless power transfer device thatmake the phase/amplitude map of the notional field quasi-parallel to theplane of the aperture of the transmitting wireless power transferdevice.
 20. The method of claim 10, wherein the phase/amplitude map ofthe notional field comprises coherent phase.
 21. A system comprising:one or more computers and one or more storage devices storinginstructions which are operable, when executed by the one or morecomputers, to cause the one or more computers to perform operationscomprising: generating a spatial frequency representation of a notionalfield in a plane of an aperture of a first wireless power transferdevice; determining a phase/amplitude map for a second notional field ina plane of an aperture of a second wireless power transfer device basedon the spatial frequency representation of the notional field in theplane of the aperture of the first wireless power transfer device and aposition of the first wireless power transfer device relative to thesecond wireless power transfer device; and generating control signalsfor one or more transducer elements of the second wireless powertransfer device based on the determined phase/amplitude map for thesecond notional field in the plane of the aperture of the secondwireless power transfer device.